Buggy python submission (verdict: Time Limit Exceeded):
import sys
from fractions import gcd
def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        div = 2
        while _gcd > 1:
            if _gcd % div == 0:
                while _gcd % div == 0:
                    _gcd /= div
                cnt += 1
            if div > 2:
              div += 2
            else:
              div += 1
        #print(memo_set)
        print(cnt + 1)

if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Runtime Error):
import sys
from fractions import gcd
def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        div = 2
        while _gcd > 1:
            if _gcd % div == 0:
                while _gcd % div == 0:
                    _gcd /= div
                cnt += 1
            if div > 2:
              div += 2
            else:
	          div += 1
        #print(memo_set)
        print(cnt + 1)

if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from fractions import gcd
def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        div = 2
        while _gcd > 1:
            if _gcd % div == 0:
                while _gcd % div == 0:
                    _gcd /= div
                cnt += 1
            div += 1
        #print(memo_set)
        print(cnt + 1)

if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Runtime Error):
import sys
import random
import numpy as np
from fractions import gcd
def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    memo_ls = np.zeros(_gcd).flatten()
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        for i in range(2, _gcd+1):
            if _gcd % i == 0 and memo_ls[i-1] != 1:
                #memo_ls[i-1::i] = 1
                cnt += 1
                #memo_set.add(i)
        #print(memo_set)
        print(cnt + 1)

if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Runtime Error):
import sys
import random
import numpy as np
from fractions import gcd
def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    memo_ls = np.zeros(_gcd).flatten()
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        for i in range(2, _gcd+1):
            if _gcd % i == 0 and memo_ls[i-1] != 1:
                memo_ls[i-1::i] = 1
                cnt += 1
                #memo_set.add(i)
        #print(memo_set)
        print(cnt + 1)

if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Runtime Error):
import sys
import numpy as np
from fractions import gcd
a, b = [int(i) for i in sys.stdin.readline().split()]
_gcd = gcd(a,b)
memo_ls = np.zeros(_gcd).flatten()
#memo_set = set()
cnt = 0
if _gcd == 1:
    print(1)
else:
    for i in range(2, _gcd+1):
        if _gcd % i == 0 and memo_ls[i-1] != 1:
            memo_ls[i-1::i] = 1
            cnt += 1
            #memo_set.add(i)
    #print(memo_set)
    print(cnt + 1)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Runtime Error):
import sys
import numpy as np
from fractions import gcd
a, b = [int(i) for i in sys.stdin.readline().split()]
_gcd = gcd(a,b)
memo_ls = np.zeros(_gcd+1)
#memo_set = set()
cnt = 0
if _gcd == 1:
    print(1)
else:
    for i in range(2, _gcd+1):
        if _gcd % i == 0 and memo_ls[i-1] != 1:
            memo_ls[i-1::i] = 1
            cnt += 1
            #memo_set.add(i)
    #print(memo_set)
    print(cnt + 1)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Runtime Error):
import sys
import numpy as np
from fractions import gcd
a, b = [int(i) for i in sys.stdin.readline().split()]
_gcd = gcd(a,b)
memo_ls = np.zeros(_gcd)
#memo_set = set()
cnt = 0
if _gcd == 1:
    print(1)
else:
    for i in range(2, _gcd+1):
        if _gcd % i == 0 and memo_ls[i-1] != 1:
            memo_ls[i-1::i] = 1
            cnt += 1
            #memo_set.add(i)
    #print(memo_set)
    print(cnt + 1)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Runtime Error):
import sys
import numpy as np
from fractions import gcd
a, b = [int(i) for i in sys.stdin.readline().split()]
_gcd = gcd(a,b)
memo_ls = np.zeros(_gcd)
#memo_set = set()
cnt = 0
if gcd == 1:
    print(1)
else:
    for i in range(2, _gcd):
        if _gcd % i == 0 and memo_ls[i-1] != 1:
            memo_ls[i-1::i] = 1
            cnt += 1
            #memo_set.add(i)
    #print(memo_set)
    print(cnt + 1)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Runtime Error):
import sys
import numpy as np
from fractions import gcd
a, b = [int(i) for i in sys.stdin.readline().split()]
_gcd = gcd(a,b)
memo_ls = np.zeros(_gcd)
#memo_set = set()
cnt = 0
if gcd == 1:
    print(1)
else:
    for i in range(2, _gcd+1):
        if _gcd % i == 0 and memo_ls[i-1] != 1:
            memo_ls[i-1::i] = 1
            cnt += 1
            #memo_set.add(i)
    #print(memo_set)
    print(cnt + 1)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Runtime Error):
import sys
import numpy as np
from fractions import gcd
a, b = [int(i) for i in sys.stdin.readline().split()]
_gcd = gcd(a,b)
memo_ls = np.zeros(_gcd)
#memo_set = set()
cnt = 0
for i in range(2, _gcd):
    if _gcd % i == 0 and memo_ls[i-1] != 1:
        memo_ls[i-1::i] = 1
        cnt += 1
        #memo_set.add(i)
#print(memo_set)
print(cnt + 1)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Time Limit Exceeded):
import math
import sys
a, b = [int(i) for i in sys.stdin.readline().split()]

class Prime:
    seed_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
    seed_primes = [int(i) for i in "2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 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80407 80429 80447 80449 80471 80473 80489 80491 80513 80527 80537 80557 80567 80599 80603 80611 80621 80627 80629 80651 80657 80669 80671 80677 80681 80683 80687 80701 80713 80737 80747 80749 80761 80777 80779 80783 80789 80803 80809 80819 80831 80833 80849 80863 80897 80909 80911 80917 80923 80929 80933 80953 80963 80989 81001 81013 81017 81019 81023 81031 81041 81043 81047".split()]
    def is_prime(self, n):
        """
        prime test (hybrid)

        see also: https://qiita.com/gushwell/items/ff9ed83ba55350aaa369

        :param n:
        :return: boolean
        """
        is_prime_common = self.is_prime_common(n)
        if is_prime_common is not None:
            return is_prime_common

        if n < 2000000:
            return self.is_prime_brute_force(n)
        else:
            return self.is_prime_miller_rabin(n)

    def is_prime_common(self, n):
        if n == 1: return False
        if n in Prime.seed_primes: return True
        if any(map(lambda x: n % x == 0, self.seed_primes)): return False

    def is_prime_brute_force(self, n):
        """
        brute force prime test
        use with is_prime_common if you want to skip seed_primes

        :param n:
        :return: boolean
        """
        for k in range(2, int(math.sqrt(n)) + 1):
            if n % k == 0:
                return False
        return True

    def is_prime_miller_rabin(self, n):
        """
        miller rabin prime test
        use with is_prime_common if you want to skip seed_primes

        see also
            algorithm: https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test
            implementation: https://qiita.com/srtk86/items/609737d50c9ef5f5dc59
            improvement: https://qiita.com/gushwell/items/ff9ed83ba55350aaa369

        :param n:
        :return: boolean
        """

        d = n - 1
        while d & 1 == 0:
            d >>= 1

        # use one of these lines / upper is more efficient.
        witnesses = self.get_witnesses(n)
        # witnesses = [random.randint(1, n - 1) for _ in range(100)]

        for w in witnesses:
            y = pow(w, d, n)

            while d != n - 1 and y != 1 and y != n - 1:
                y = (y * y) % n
                d <<= 1

            if y != n - 1 and d & 1 == 0:
                return False

        return True

    def get_witnesses(self, num):
        def _get_range(num):
            if num < 2047:
                return 1
            if num < 1373653:
                return 2
            if num < 25326001:
                return 3
            if num < 3215031751:
                return 4
            if num < 2152302898747:
                return 5
            if num < 3474749660383:
                return 6
            if num < 341550071728321:
                return 7
            if num < 3825123056546413051:
                return 9
            return 12

        return self.seed_primes[:_get_range(num)]

    def gcd(self, a, b):
        if a < b:
            return self.gcd(b, a)
        if b == 0:
            return a
        while b:
            a, b = b, a % b
        return a

    @staticmethod
    def f(x, n, seed):
        """
        pseudo prime generator
        :param x:
        :param n:
        :param seed:
        :return: pseudo prime
        """
        p = Prime.seed_primes[seed % len(Prime.seed_primes)]
        return (p * x + seed) % n

    def find_factor(self, n, seed=1):
        """
        find one of factor of n
        this function is based to Pollard's rho algorithm

        see also
            algorithm: https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm
            implementation: https://qiita.com/gushwell/items/561afde2e00bf3380c98

        :param n:
        :param seed:
        :return: factor
        """
        if self.is_prime(n):
            return n

        x, y, d = 2, 2, 1
        count = 0
        while d == 1:
            count += 1
            x = self.f(x, n, seed)
            y = self.f(self.f(y, n, seed), n, seed)
            d = self.gcd(abs(x - y), n)

        if d == n:
            return self.find_factor(n, seed + 1)
        return self.find_factor(d)

    def find_factors(self, n):
        primes = {}
        if self.is_prime(n):
            primes[n] = 1
            return primes

        while n > 1:
            factor = self.find_factor(n)

            primes.setdefault(factor, 0)
            primes[factor] += 1

            n //= factor

        return primes


prime = Prime()
_gcd = prime.gcd(a, b)
fact_dict = prime.find_factors(_gcd)
print(len(fact_dict.keys()) + 1)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Time Limit Exceeded):
import math
import sys
a, b = [int(i) for i in sys.stdin.readline().split()]

class Prime:
    seed_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
    seed_primes = [int(i) for i in "2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 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    def is_prime(self, n):
        """
        prime test (hybrid)

        see also: https://qiita.com/gushwell/items/ff9ed83ba55350aaa369

        :param n:
        :return: boolean
        """
        is_prime_common = self.is_prime_common(n)
        if is_prime_common is not None:
            return is_prime_common

        if n < 2000000:
            return self.is_prime_brute_force(n)
        else:
            return self.is_prime_miller_rabin(n)

    def is_prime_common(self, n):
        if n == 1: return False
        if n in Prime.seed_primes: return True
        if any(map(lambda x: n % x == 0, self.seed_primes)): return False

    def is_prime_brute_force(self, n):
        """
        brute force prime test
        use with is_prime_common if you want to skip seed_primes

        :param n:
        :return: boolean
        """
        for k in range(2, int(math.sqrt(n)) + 1):
            if n % k == 0:
                return False
        return True

    def is_prime_miller_rabin(self, n):
        """
        miller rabin prime test
        use with is_prime_common if you want to skip seed_primes

        see also
            algorithm: https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test
            implementation: https://qiita.com/srtk86/items/609737d50c9ef5f5dc59
            improvement: https://qiita.com/gushwell/items/ff9ed83ba55350aaa369

        :param n:
        :return: boolean
        """

        d = n - 1
        while d & 1 == 0:
            d >>= 1

        # use one of these lines / upper is more efficient.
        witnesses = self.get_witnesses(n)
        # witnesses = [random.randint(1, n - 1) for _ in range(100)]

        for w in witnesses:
            y = pow(w, d, n)

            while d != n - 1 and y != 1 and y != n - 1:
                y = (y * y) % n
                d <<= 1

            if y != n - 1 and d & 1 == 0:
                return False

        return True

    def get_witnesses(self, num):
        def _get_range(num):
            if num < 2047:
                return 1
            if num < 1373653:
                return 2
            if num < 25326001:
                return 3
            if num < 3215031751:
                return 4
            if num < 2152302898747:
                return 5
            if num < 3474749660383:
                return 6
            if num < 341550071728321:
                return 7
            if num < 3825123056546413051:
                return 9
            return 12

        return self.seed_primes[:_get_range(num)]

    def gcd(self, a, b):
        if a < b:
            return self.gcd(b, a)
        if b == 0:
            return a
        while b:
            a, b = b, a % b
        return a

    @staticmethod
    def f(x, n, seed):
        """
        pseudo prime generator
        :param x:
        :param n:
        :param seed:
        :return: pseudo prime
        """
        p = Prime.seed_primes[seed % len(Prime.seed_primes)]
        return (p * x + seed) % n

    def find_factor(self, n, seed=1):
        """
        find one of factor of n
        this function is based to Pollard's rho algorithm

        see also
            algorithm: https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm
            implementation: https://qiita.com/gushwell/items/561afde2e00bf3380c98

        :param n:
        :param seed:
        :return: factor
        """
        if self.is_prime(n):
            return n

        x, y, d = 2, 2, 1
        count = 0
        while d == 1:
            count += 1
            x = self.f(x, n, seed)
            y = self.f(self.f(y, n, seed), n, seed)
            d = self.gcd(abs(x - y), n)

        if d == n:
            return self.find_factor(n, seed + 1)
        return self.find_factor(d)

    def find_factors(self, n):
        primes = {}
        if self.is_prime(n):
            primes[n] = 1
            return primes

        while n > 1:
            factor = self.find_factor(n)

            primes.setdefault(factor, 0)
            primes[factor] += 1

            n //= factor

        return primes


prime = Prime()
if prime.is_prime(a) and prime.is_prime(b):
    print(1)
else:
    _gcd = prime.gcd(a, b)
    fact_dict = prime.find_factors(_gcd)
    print(len(fact_dict.keys()) + 1)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Time Limit Exceeded):
import math
import sys
a, b = [int(i) for i in sys.stdin.readline().split()]

class Prime:
    seed_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
    seed_primes = [int(i) for i in "2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 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    def is_prime(self, n):
        """
        prime test (hybrid)

        see also: https://qiita.com/gushwell/items/ff9ed83ba55350aaa369

        :param n:
        :return: boolean
        """
        is_prime_common = self.is_prime_common(n)
        if is_prime_common is not None:
            return is_prime_common

        if n < 2000000:
            return self.is_prime_brute_force(n)
        else:
            return self.is_prime_miller_rabin(n)

    def is_prime_common(self, n):
        if n == 1: return False
        if n in Prime.seed_primes: return True
        if any(map(lambda x: n % x == 0, self.seed_primes)): return False

    def is_prime_brute_force(self, n):
        """
        brute force prime test
        use with is_prime_common if you want to skip seed_primes

        :param n:
        :return: boolean
        """
        for k in range(2, int(math.sqrt(n)) + 1):
            if n % k == 0:
                return False
        return True

    def is_prime_miller_rabin(self, n):
        """
        miller rabin prime test
        use with is_prime_common if you want to skip seed_primes

        see also
            algorithm: https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test
            implementation: https://qiita.com/srtk86/items/609737d50c9ef5f5dc59
            improvement: https://qiita.com/gushwell/items/ff9ed83ba55350aaa369

        :param n:
        :return: boolean
        """

        d = n - 1
        while d & 1 == 0:
            d >>= 1

        # use one of these lines / upper is more efficient.
        witnesses = self.get_witnesses(n)
        # witnesses = [random.randint(1, n - 1) for _ in range(100)]

        for w in witnesses:
            y = pow(w, d, n)

            while d != n - 1 and y != 1 and y != n - 1:
                y = (y * y) % n
                d <<= 1

            if y != n - 1 and d & 1 == 0:
                return False

        return True

    def get_witnesses(self, num):
        def _get_range(num):
            if num < 2047:
                return 1
            if num < 1373653:
                return 2
            if num < 25326001:
                return 3
            if num < 3215031751:
                return 4
            if num < 2152302898747:
                return 5
            if num < 3474749660383:
                return 6
            if num < 341550071728321:
                return 7
            if num < 3825123056546413051:
                return 9
            return 12

        return self.seed_primes[:_get_range(num)]

    def gcd(self, a, b):
        if a < b:
            return self.gcd(b, a)
        if b == 0:
            return a
        while b:
            a, b = b, a % b
        return a

    @staticmethod
    def f(x, n, seed):
        """
        pseudo prime generator
        :param x:
        :param n:
        :param seed:
        :return: pseudo prime
        """
        p = Prime.seed_primes[seed % len(Prime.seed_primes)]
        return (p * x + seed) % n

    def find_factor(self, n, seed=1):
        """
        find one of factor of n
        this function is based to Pollard's rho algorithm

        see also
            algorithm: https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm
            implementation: https://qiita.com/gushwell/items/561afde2e00bf3380c98

        :param n:
        :param seed:
        :return: factor
        """
        if self.is_prime(n):
            return n

        x, y, d = 2, 2, 1
        count = 0
        while d == 1:
            count += 1
            x = self.f(x, n, seed)
            y = self.f(self.f(y, n, seed), n, seed)
            d = self.gcd(abs(x - y), n)

        if d == n:
            return self.find_factor(n, seed + 1)
        return self.find_factor(d)

    def find_factors(self, n):
        primes = {}
        if self.is_prime(n):
            primes[n] = 1
            return primes

        while n > 1:
            factor = self.find_factor(n)

            primes.setdefault(factor, 0)
            primes[factor] += 1

            n //= factor

        return primes


prime = Prime()
if prime.is_prime(a) and prime.is_prime(b):
    print(1)
else:
    _gcd = prime.gcd(a, b)
    fact_dict = prime.find_factors(_gcd)
    print(len(fact_dict.keys()) + 1)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Time Limit Exceeded):
import math

a, b = [int(i) for i in input().split()]


class Prime:
    seed_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
    seed_primes = [int(i) for i in "2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 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    def is_prime(self, n):
        """
        prime test (hybrid)

        see also: https://qiita.com/gushwell/items/ff9ed83ba55350aaa369

        :param n:
        :return: boolean
        """
        is_prime_common = self.is_prime_common(n)
        if is_prime_common is not None:
            return is_prime_common

        if n < 2000000:
            return self.is_prime_brute_force(n)
        else:
            return self.is_prime_miller_rabin(n)

    def is_prime_common(self, n):
        if n == 1: return False
        if n in Prime.seed_primes: return True
        if any(map(lambda x: n % x == 0, self.seed_primes)): return False

    def is_prime_brute_force(self, n):
        """
        brute force prime test
        use with is_prime_common if you want to skip seed_primes

        :param n:
        :return: boolean
        """
        for k in range(2, int(math.sqrt(n)) + 1):
            if n % k == 0:
                return False
        return True

    def is_prime_miller_rabin(self, n):
        """
        miller rabin prime test
        use with is_prime_common if you want to skip seed_primes

        see also
            algorithm: https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test
            implementation: https://qiita.com/srtk86/items/609737d50c9ef5f5dc59
            improvement: https://qiita.com/gushwell/items/ff9ed83ba55350aaa369

        :param n:
        :return: boolean
        """

        d = n - 1
        while d & 1 == 0:
            d >>= 1

        # use one of these lines / upper is more efficient.
        witnesses = self.get_witnesses(n)
        # witnesses = [random.randint(1, n - 1) for _ in range(100)]

        for w in witnesses:
            y = pow(w, d, n)

            while d != n - 1 and y != 1 and y != n - 1:
                y = (y * y) % n
                d <<= 1

            if y != n - 1 and d & 1 == 0:
                return False

        return True

    def get_witnesses(self, num):
        def _get_range(num):
            if num < 2047:
                return 1
            if num < 1373653:
                return 2
            if num < 25326001:
                return 3
            if num < 3215031751:
                return 4
            if num < 2152302898747:
                return 5
            if num < 3474749660383:
                return 6
            if num < 341550071728321:
                return 7
            if num < 3825123056546413051:
                return 9
            return 12

        return self.seed_primes[:_get_range(num)]

    def gcd(self, a, b):
        if a < b:
            return self.gcd(b, a)
        if b == 0:
            return a
        while b:
            a, b = b, a % b
        return a

    @staticmethod
    def f(x, n, seed):
        """
        pseudo prime generator
        :param x:
        :param n:
        :param seed:
        :return: pseudo prime
        """
        p = Prime.seed_primes[seed % len(Prime.seed_primes)]
        return (p * x + seed) % n

    def find_factor(self, n, seed=1):
        """
        find one of factor of n
        this function is based to Pollard's rho algorithm

        see also
            algorithm: https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm
            implementation: https://qiita.com/gushwell/items/561afde2e00bf3380c98

        :param n:
        :param seed:
        :return: factor
        """
        if self.is_prime(n):
            return n

        x, y, d = 2, 2, 1
        count = 0
        while d == 1:
            count += 1
            x = self.f(x, n, seed)
            y = self.f(self.f(y, n, seed), n, seed)
            d = self.gcd(abs(x - y), n)

        if d == n:
            return self.find_factor(n, seed + 1)
        return self.find_factor(d)

    def find_factors(self, n):
        primes = {}
        if self.is_prime(n):
            primes[n] = 1
            return primes

        while n > 1:
            factor = self.find_factor(n)

            primes.setdefault(factor, 0)
            primes[factor] += 1

            n //= factor

        return primes


prime = Prime()
_gcd = prime.gcd(a, b)
fact_dict = prime.find_factors(_gcd)
print(len(fact_dict.keys()) + 1)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)

Buggy python submission (verdict: Time Limit Exceeded):
import math

a, b = [int(i) for i in input().split()]


class Prime:
    seed_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
    seed_primes = [int(i) for i in "2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 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40169 40177 40189 40193 40213 40231 40237 40241 40253 40277 40283 40289 40343 40351 40357 40361 40387 40423 40427 40429 40433 40459 40471 40483 40487 40493 40499 40507 40519 40529 40531 40543 40559 40577 40583 40591 40597 40609 40627 40637 40639 40693 40697 40699 40709 40739 40751 40759 40763 40771 40787 40801 40813 40819 40823 40829 40841 40847 40849 40853 40867 40879 40883 40897 40903 40927 40933 40939 40949 40961 40973 40993 41011 41017 41023 41039 41047 41051 41057 41077 41081 41113 41117 41131 41141 41143 41149 41161 41177 41179 41183 41189 41201 41203 41213 41221 41227 41231 41233 41243 41257 41263 41269 41281 41299 41333 41341 41351 41357 41381 41387 41389 41399 41411 41413 41443 41453 41467 41479 41491 41507 41513 41519 41521 41539 41543 41549 41579 41593 41597 41603 41609 41611 41617 41621 41627 41641 41647 41651 41659 41669 41681 41687 41719 41729 41737 41759 41761 41771 41777 41801 41809 41813 41843 41849 41851 41863 41879 41887 41893 41897 41903 41911 41927 41941 41947 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47363 47381 47387 47389 47407 47417 47419 47431 47441 47459 47491 47497 47501 47507 47513 47521 47527 47533 47543 47563 47569 47581 47591 47599 47609 47623 47629 47639 47653 47657 47659 47681 47699 47701 47711 47713 47717 47737 47741 47743 47777 47779 47791 47797 47807 47809 47819 47837 47843 47857 47869 47881 47903 47911 47917 47933 47939 47947 47951 47963 47969 47977 47981 48017".split()]
    def is_prime(self, n):
        """
        prime test (hybrid)

        see also: https://qiita.com/gushwell/items/ff9ed83ba55350aaa369

        :param n:
        :return: boolean
        """
        is_prime_common = self.is_prime_common(n)
        if is_prime_common is not None:
            return is_prime_common

        if n < 2000000:
            return self.is_prime_brute_force(n)
        else:
            return self.is_prime_miller_rabin(n)

    def is_prime_common(self, n):
        if n == 1: return False
        if n in Prime.seed_primes: return True
        if any(map(lambda x: n % x == 0, self.seed_primes)): return False

    def is_prime_brute_force(self, n):
        """
        brute force prime test
        use with is_prime_common if you want to skip seed_primes

        :param n:
        :return: boolean
        """
        for k in range(2, int(math.sqrt(n)) + 1):
            if n % k == 0:
                return False
        return True

    def is_prime_miller_rabin(self, n):
        """
        miller rabin prime test
        use with is_prime_common if you want to skip seed_primes

        see also
            algorithm: https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test
            implementation: https://qiita.com/srtk86/items/609737d50c9ef5f5dc59
            improvement: https://qiita.com/gushwell/items/ff9ed83ba55350aaa369

        :param n:
        :return: boolean
        """

        d = n - 1
        while d & 1 == 0:
            d >>= 1

        # use one of these lines / upper is more efficient.
        witnesses = self.get_witnesses(n)
        # witnesses = [random.randint(1, n - 1) for _ in range(100)]

        for w in witnesses:
            y = pow(w, d, n)

            while d != n - 1 and y != 1 and y != n - 1:
                y = (y * y) % n
                d <<= 1

            if y != n - 1 and d & 1 == 0:
                return False

        return True

    def get_witnesses(self, num):
        def _get_range(num):
            if num < 2047:
                return 1
            if num < 1373653:
                return 2
            if num < 25326001:
                return 3
            if num < 3215031751:
                return 4
            if num < 2152302898747:
                return 5
            if num < 3474749660383:
                return 6
            if num < 341550071728321:
                return 7
            if num < 3825123056546413051:
                return 9
            return 12

        return self.seed_primes[:_get_range(num)]

    def gcd(self, a, b):
        if a < b:
            return self.gcd(b, a)
        if b == 0:
            return a
        while b:
            a, b = b, a % b
        return a

    @staticmethod
    def f(x, n, seed):
        """
        pseudo prime generator
        :param x:
        :param n:
        :param seed:
        :return: pseudo prime
        """
        p = Prime.seed_primes[seed % len(Prime.seed_primes)]
        return (p * x + seed) % n

    def find_factor(self, n, seed=1):
        """
        find one of factor of n
        this function is based to Pollard's rho algorithm

        see also
            algorithm: https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm
            implementation: https://qiita.com/gushwell/items/561afde2e00bf3380c98

        :param n:
        :param seed:
        :return: factor
        """
        if self.is_prime(n):
            return n

        x, y, d = 2, 2, 1
        count = 0
        while d == 1:
            count += 1
            x = self.f(x, n, seed)
            y = self.f(self.f(y, n, seed), n, seed)
            d = self.gcd(abs(x - y), n)

        if d == n:
            return self.find_factor(n, seed + 1)
        return self.find_factor(d)

    def find_factors(self, n):
        primes = {}
        if self.is_prime(n):
            primes[n] = 1
            return primes

        while n > 1:
            factor = self.find_factor(n)

            primes.setdefault(factor, 0)
            primes[factor] += 1

            n //= factor

        return primes


prime = Prime()
if prime.is_prime(a) and prime.is_prime(b):
    print(1)
else:
    _gcd = prime.gcd(a, b)
    fact_dict = prime.find_factors(_gcd)
    print(len(fact_dict.keys()) + 1)

Fixed submission:
import sys
from fractions import gcd
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a

def main(a, b):
    #a, b = [int(i) for i in sys.stdin.readline().split()]
    _gcd = gcd(a,b)
    #memo_ls = [0 for i in range(_gcd)]
    #memo_set = set()
    cnt = 0
    if _gcd == 1:
        print(1)
    else:
        res = prime_factorize(_gcd)
        print(len(res) + 1)
if __name__ == "__main__":
    a, b = [int(i) for i in sys.stdin.readline().split()]
    main(a, b)