Problem:
 Score : 400 points    Problem Statement Given are positive integers A and B .  Let us choose some number of positive common divisors of A and B .  Here, any two of the chosen divisors must be coprime.  At most, how many divisors can we choose?  Definition of common divisor  An integer d is said to be a common divisor of integers x and y when d divides both x and y .   Definition of being coprime  Integers x and y are said to be coprime when x and y have no positive common divisors other than 1 .   Definition of dividing  An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x .       Constraints  All values in input are integers.  1 \leq A, B \leq 10^{12}         Input Input is given from Standard Input in the following format:  A  B       Output Print the maximum number of divisors that can be chosen to satisfy the condition.        Sample Input 1 12 18      Sample Output 1 3  12 and 18 have the following positive common divisors: 1 , 2 , 3 , and 6 .  1 and 2 are coprime, 2 and 3 are coprime, and 3 and 1 are coprime, so we can choose 1 , 2 , and 3 , which achieve the maximum result.       Sample Input 2 420 660      Sample Output 2 4       Sample Input 3 1 2019      Sample Output 3 1  1 and 2019 have no positive common divisors other than 1 .

Solution (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    from copy import deepcopy, copy 
    import operator
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd 
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    
        
        
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    R = lambda: list(map(int, r().split()))
    Rmap = lambda: map(int, r().split())
    Rfloat = lambda: list(map(float, r().split()))
    Rtuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
        
    
    

    A, B = R()
    
    U = make_divisors(gcd(A, B))
    cnt = 0
    for u in U:
        if len(make_divisors(u)) == 2:
            cnt += 1
    print(cnt+1)

    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    
    >>> a = 5
    >>> bin_str_a = format(a, '
    >>> print(bin_str_a)
    0b0101 
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Solution (Python):
a, b = map(int, input().split())

def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)

g = gcd(a, b)

i = 2
count = 1
m = gcd(a, b)
while i * i <= g:
    if m % i == 0:
        count += 1
    while m % i == 0:
        m = m // i
    i += 1

if m > 1:
    count += 1

print(count)

Solution (Python):
import sys
input=sys.stdin.readline
a,b=map(int,input().split())
import fractions
c=fractions.gcd(a,b)
res=[]
i=2
while i**2<=c:
    if c%i==0:
        c=c//i
        res.append([i,1])
    while c%i==0:
        c=c//i
        res[-1][1]+=1
    i=i+1
if not c==1:
    res.append([c,1])
m=len(res)
ans=m+1
print(ans)

Solution (Python):
A, B = map(int, input().split())

common_divisors = []
for n in range(1, int(min(A, B) ** 0.5) + 1):
    if (A % n == 0) & (B % n == 0):
        common_divisors.append(n)

    if A % n == 0:
        x = A // n
        if B % x == 0:
            common_divisors.append(x)



def is_prime(n):
    if n == 1:
        return False

    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            return False
    else:
        return True


ans = 0
for cd in common_divisors:
    ans += is_prime(cd)

print(ans + 1)

Solution (Python):





def gcd(a, b):
  while b != 0:
    a, b = b, a % b

  return a



def factorization(n):
  arr = []
  temp = n

  for i in range(2, int(-(-n ** 0.5 // 1)) + 1):
    if temp % i == 0:
      cnt = 0
      while temp % i == 0:
        cnt += 1
        temp //= i
      arr.append([i, cnt])

  if temp != 1:
    arr.append([temp, 1])

  if arr == []:
    arr.append([n, 1])

  return arr


def main():
  a, b = map(int, input().split())
  g = gcd(a, b)
  fs = [v for v, _ in factorization(g) if v != 1]
  print(len(fs) + 1)


if __name__ == '__main__':
  main()

Solution (Python):
from collections import deque
import sys
sys.setrecursionlimit(10**7)
input = sys.stdin.readline
def isprime(n):
  for i in range(2,int(n**0.5)+1):
    if n%i == 0:
      return False
  return True
 
def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)
    divisors.sort()
    return divisors
from fractions import gcd
def coprime(a, b):
    return gcd(a, b) == 1


def solve():
  a,b = (int(i) for i in input().split())
  ad = make_divisors(a)
  bd = make_divisors(b)
  act = []
  bct = []
  for i in ad:
    if isprime(i):
      act.append(i)
  for j in bd:
      if isprime(j):
        bct.append(j)
  ct = 0
  for i in act:
    if i in bct:
      ct += 1
  print(ct)
solve()

Solution (Python):
import fractions
def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a
a,b=map(int,input().split())
ans=0
c=fractions.gcd(a,b)
d=prime_factorize(c)
d=set(d)
print(len(d)+1)

Solution (Python):
def prime_decomposition(n):
  i = 2
  d = {}
  while i * i <= n:
    while n % i == 0:
      n //= i
      if i not in d:
          d[i] = 0
      d[i] += 1
    i += 1
  if n > 1:
    if n not in d:
        d[n] = 1
  return d

def gcd(a, b):
	while b:
		a, b = b, a % b
	return a

A,B = map(int,input().split())
d = gcd(A,B)
p = prime_decomposition(d)
ans = 1
for i in p:
    ans += 1
print(ans)

Solution (Python):
from fractions import gcd

A, B = map(int, input().split())

d = gcd(A, B)
d_ori = d
ans = 1
k = 2
while d > 2:
    plus = 0
    while d % k == 0:
        d //= k
        plus = 1
    ans += plus
    k += 1
    if k > d_ori**(1/2):
        ans += 1
        break
print(ans)

Solution (Python):
inpl = lambda: list(map(int,input().split()))

def gcd(a, b):
    if a < 0: a = -a
    if b < 0: b = -b
    while b > 0:
        (a, b) = (b, a % b)
    return a

import math
def primes(N):
    P = []
    for i in range(2,N):
        sieve = 1
        for p in P:
            if p*p > i:
                break
            elif i % p == 0:
                sieve = 0
                break
        if sieve == 0:
            continue
        else:
            P.append(i)
    return P

def factorize(n, P=None):
    if P is None:
        P = primes(int(math.sqrt(n))+1)
    factor = []
    power = []
    for p in P:
        if p * p > n:
            break
        elif n % p == 0:
            k = 0
            while n % p == 0:
                n //= p
                k += 1
            factor.append(p)
            power.append(k)
    if n > 1:
        factor.append(n)
        power.append(1)
    return factor, power

A, B = inpl()
C = gcd(A,B)
factor, _ = factorize(C)
print(len(factor)+1)

Solution (Python):

(N,M) = (int(i) for i in input().split(" "))
(N,M)=(min(M,N),max(M,N))
while M%N!=0:
	M=M%N
	(N,M)=(min(M,N),max(M,N))
i = 2
ans = 0
DN = N
while i*i <= DN :
	if N%i==0:
		ans += 1
		while N%i==0:
			N/=i
	i+=1
if i <= N:
	ans +=1
print(ans+1)

Solution (Python):
def gcd(a,b):
  while b!=0:
    a,b=b,a%b
  return a

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

def solve():
  A, B = map(int, input().split())
  return len(set(prime_factorize(gcd(A, B)))) + 1

print(solve())

Solution (Python):
import math



A, B = map(int, input().split())


def gcd(a, b):
    if a < b:
        a, b = b, a
    if b == 0:
        return a
    else:
        return gcd(b, a % b)


def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)
    return divisors


def is_prime(n):
    if n == 1:
        return True

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

    return True


print(sum([is_prime(n) for n in make_divisors(gcd(A, B))]))

Solution (Python):
def divisor(n): 
    i = 1
    table = []
    while i * i <= n:
        if n%i == 0:
            table.append(i)
            table.append(n//i)
        i += 1
    table = list(set(table))
    return table


def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

def is_prime(n):
    for i in range(2, n + 1):
        if i * i > n:
            break
        if n % i == 0:
            return False
    return n != 1

a, b = map(int, input().split())

a_div = divisor(a)
b_div = divisor(b)
ans = set(a_div) & set(b_div)

count = 0
for i in ans:
    if is_prime(i):
        count += 1

print(count + 1)

Solution (Python):

import sys
from collections import deque, defaultdict
import copy
import bisect
sys.setrecursionlimit(10 ** 9)
import math
import heapq
from itertools import product, permutations,combinations
import fractions

import sys
def input():
	return sys.stdin.readline().strip()

def soinsu_bunkai(n):
	ans = []
	num = n
	i = 2
	while i <= n**0.5:
		if num % i == 0:
			if len(ans) == 0 or ans[-1][0] != i:
				ans.append([i, 1])
			else:
				ans[-1][1] += 1
			num = num//i
		else:
			i+=1
	if num != 1:
		ans.append([num, 1])

	return ans

A, B = list(map(int, input().split()))

C = fractions.gcd(A, B)

C_list = soinsu_bunkai(C)

print(len(C_list) + 1)

Solution (Python):

from fractions import gcd
a, b = map(int, input().split())
g = gcd(a, b)
ans = {}
for i in range(2, int(g**0.5 + 1)):
    while g % i == 0:
        ans[i] = ans[i] + 1 if i in ans else 1
        g //= i
if g != 1:
    ans[g] = 1
print(len(ans) + 1)

Solution (Python):

from collections import defaultdict, deque
from heapq import heappush, heapreplace
from itertools import count
from math import ceil, sqrt
from fractions import gcd


class Primes_C(object):

    def b_search(L,t):
        
        search_range = [-1, len(L)]
        update_range = lambda mid: search_range.__setitem__(t<L[mid], mid)
        for _ in range(search_range[1].bit_length()):
            update_range(sum(search_range)//2)
        return search_range[0]
    
    def __init__(self):
        self.P = [2]
        self.Pappend = self.P.append
        self.Q = deque([])
        self.Qappend = self.Q.append
        self.Qpopleft = self.Q.popleft
        self.hq = [] 
        self.integer = count(3,2)
        self.current_i = 2
        self.valid_range = 1
        self.iter_index = 0

    def __iter__(self):
        return self

    def __next__(self):
        if self.iter_index >= len(self.P):
            self.step_calc(1)
        self.iter_index += 1
        return self.P[self.iter_index-1]

    def iter_reset(self, index=0):
        self.iter_index = index

    def list(self, max_int=None):
        if max_int is None:
            return self.P[:]

        elif  max_int <= self.current_i:
            return self.P[:Primes_C.b_search(self.P,max_int)+1]

        else:
            self.calc(max_int)
            return self.P[:]

    def extend(self, i):
        if i >= self.valid_range:
            if self.Q:
                q = self.Qpopleft()
                heappush(self.hq, (q**2,q))
            self.valid_range = self.Q[0]**2 if self.Q else i**2

    def check_update(self,i):
        m,r = self.hq[0] if self.hq else (0,0)
        flag =  (i != m)
        if flag:
            self.Pappend(i)
            self.Qappend(i)
        while m == i:
            heapreplace(self.hq, (m+2*r, r))
            m,r = self.hq[0]
        return flag

    def calc(self, max_int):
        for i in self.integer:
            self.extend(i)
            self.check_update(i) 
            self.current_i = i+1
            if max_int <= self.current_i:
                break

    def step_calc(self, step):
        for i in self.integer:
            self.extend(i)
            step -= self.check_update(i) 
            self.current_i = i+1
            if not step:
                break

    def factorization(self, m, F=defaultdict(int), break_flag=False):
        if m <= 0:
            raise  ValueError('m >= 1')
        iter_index = self.iter_index
        self.iter_reset()
        flag = True
        for p in self:
            if flag:
                try:
                    max_int = ceil(sqrt(m))
                except OverflowError:
                    max_int = m//p

                flag = False
            if m >= p > max_int:
                F[m] += 1
                break
            while not m%p:
                m //= p
                F[p] += 1
                flag = True
            if (flag and break_flag) or m == 1:
                break
        F_ = dict(F)
        F.clear()
        self.iter_reset(iter_index)
        return F_

    def is_prime(self,m):
        F = self.factorization(m)
        return m in F



def solve():
    A, B = map(int, input().split())
    C = gcd(A,B)    
    P = Primes_C()
    F = P.factorization(C)
    res = len(F)+1
    return str(res)

if __name__ == '__main__':
    print(solve())

Solution (Python):
import collections


def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

A, B = map(int,input().split())

gc = gcd(A, B)

c = collections.Counter(prime_factorize(gc))

print(len(c.keys()) + 1)

Solution (Python):
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,queue,copy

sys.setrecursionlimit(10**7)
inf=10**20
mod=10**9+7
dd=[(-1,0),(0,1),(1,0),(0,-1)]
ddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
def S(): return input()


def getPrimeList(n):
  l=[]
  t=int(math.sqrt(n))+1
  
  for a in range(2,t):
    while n%a==0:
      n//=a
      l.append(a)
  
  if n!=1:
    l.append(n)
  
  return l

def main():
  a,b=LI()

  if a==1 and b==1:
    return 1

  a=getPrimeList(a)
  b=getPrimeList(b)

  a=list(set(a))
  b=list(set(b))

  c=a+b
  c.sort()

  ans=1
  y=c[0]
  cnt=1
  for x in c[1:]:
    if x==y:
      cnt+=1
    else:
      y=x
      cnt=1

    if cnt==2:
      ans+=1

  return ans


print(main())

Solution (Python):
import sys
from fractions import gcd
def input():
    return sys.stdin.readline()[:-1]
a,b=map(int,input().split())
tmp=gcd(a,b)

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

ans=factorization(tmp)

if tmp==1:
    print(1)
else:
    print(len(ans)+1)

Solution (Python):
from fractions import gcd
a,b=map(int,input().split())
m=gcd(a,b)
if m==1:print(1);exit()
pf={}
for i in range(2,int(m**0.5)+1):
    while m%i==0:
        pf[i]=pf.get(i,0)+1
        m//=i
if m>1:pf[m]=1
print(len(pf.keys())+1)

Solution (Python):
import collections

A,B=map(int,input().split())

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

AA=collections.Counter(prime_factorize(A))
BB=collections.Counter(prime_factorize(B))

AAA=list(AA)
BBB=list(BB)

CCC=set(AAA) & set(BBB)

print(len(CCC)+1)

Solution (Python):
def gcd(x, y):
    if y == 0:
        return x
    else:
        return gcd(y, x % y)

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

import math

a, b = map(int, input().split())
c=gcd(a, b)
d=prime_factorize(c)
count=0
before=0
for i in range(len(d)):
    if d[i]!=before:
        count+=1
    before=d[i]

print(count+1)

Solution (Python):
A, B = map(int, input().split())

def getPrimeFactors(x):
    ans = []
    for d in range(2, int(x**0.5)+1):
        while x%d == 0:
            ans.append(d)
            x //= d
    if x != 1:
        ans.append(x)
    return ans

pfAs = [1] + getPrimeFactors(A)
pfBs = [1] + getPrimeFactors(B)

ans = len(set(pfAs) & set(pfBs))
print(ans)

Solution (Python):
a,b = (int(i) for i in input().split())
def gcd(a,b):
    if a%b: return gcd(b,a%b)
    else: return b
g = gcd(a,b)
num,ans = g,1
for i in range(2,int(g**0.5)+1):
    if num%i==0:
        ans+=1
        while num%i==0: num//=i
if num!=1: ans+=1
print(ans)

Solution (Python):
def gcd(a, b):
    while b:
        a, b = b, a % b
    return a
a,b=map(int,input().split())
sai=gcd(a,b)

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    
    return divisors

kou=make_divisors(sai)

def is_prime(n):
    if n == 1:
        return False
    for i in range(2,int(n**0.5)+1):
        if n % i == 0:
            return False
    return True

ans=0
for i in kou:
    if is_prime(i):
        ans+=1
print(ans+1)

Solution (Python):
from fractions import gcd
A, B = map(int, input().split())
g = gcd(A, B)
def prime_factor(n):
    ass = set()
    for i in range(2,int(n**0.5)+1):
        if n%i == 0:
            ass.add(i)
        while n % i==0:
            n = n//i
    if n != 1:
        ass.add(n)
    return ass
ass = prime_factor(g)
print(len(ass)+1)

Solution (Python):
MAX_PRIME = 10**6
is_prime = [1] * MAX_PRIME
primes = []
is_prime[0] = 0
is_prime[1] = 0
for i in range(MAX_PRIME):
    if is_prime[i]:
        primes.append(i)
        for j in range(2, ((MAX_PRIME-1)//i) + 1):
            is_prime[i*j] = 0

def factorization(n):
    factor = {}
    for p in primes:
        if p ** 2 > n:
            break
        while n % p == 0:
            n //= p
            if p not in factor:
                factor[p] = 1
            else:
                factor[p] += 1
    if n > 1:
        factor[n] = 1
    return factor

a, b = map(int, input().split())
ans = 1
fa = factorization(a)
fb = factorization(b)
for p, _ in fa.items():
    if p in fb:
        ans += 1
print(ans)

Solution (Python):
from fractions import*;g=gcd(*map(int,input().split()));d={};i=2
while i*i<=g:
    if g%i:i+=1
    else:g//=i;d[i]=d.get(i,0)+1
if g>1:d[g]=d.get(g,0)+1
print(len(d)+1)

Solution (Python):
import fractions
a, b= (int(i) for i in input().split())
m=fractions.gcd(a,b)

pf={}
for i in range(2,int(m**0.5)+1):
    while m%i==0:
        pf[i]=pf.get(i,0)+1
        m//=i
if m > 1:
    pf[m]=1

print(len(pf)+1)

Solution (Python):

import  numpy as np
a,b = map(int,input().split())
def factorize(N):
    up = int(np.sqrt(N))+2
    out = {}

    for i in range(2,up):
        if N%i == 0:
            temp = N
            count = 0
            while(True):
                N = N//i
                count += 1
                if N%i != 0:
                    break
            out[i] = count
        else:
            continue
    if N != 1:
        out[N] = 1
    return out

a = factorize(a)
b = factorize(b)

sa = set()
sb = set()

for t in a:
    sa.add(t)
for t in b:
    sb.add(t)

t = sa&sb
print(len(t)+1)