Buggy python submission (verdict: Time Limit Exceeded):
import fractions
import collections

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

GCD = fractions.gcd(A, B)





def primes_ordered_dict(n):
    #
    prime_list = []
    non_prime_list = []
    number_dict = collections.OrderedDict(
        ((i, None) for i in range(n + 1)))
    #
    del number_dict[0]
    del number_dict[1]
    while True:
        # get prime
        prime, _ = number_dict.popitem(False)
        if A % prime == 0 and B % prime == 0:
            prime_list.append(prime)
        # break
        if not (prime * prime <= n):
            break
        # get non primes
        non_prime_list.append(prime * prime)
        for k in number_dict:
            if prime * k <= n:
                non_prime_list.append(prime * k)
            else:
                break
        # delete non primes
        for non_prime in non_prime_list:
            del number_dict[non_prime]
        non_prime_list.clear()

    # add rest of numbers as prime
    prime_list.extend(
        [prime for prime, _ in number_dict.items() if A % prime == 0 and B % prime == 0])

    return prime_list

if GCD == 1:
    print(1)
else:
    print(len(primes_ordered_dict(GCD))+1)

Fixed submission:
import collections
import math

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


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



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

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

    return True

A_div = set(make_divisors(A))
B_div = set(make_divisors(B))
common_div = (A_div & B_div)

cnt = 1
for c in common_div:
    if is_prime(c):
        cnt += 1

print(cnt)

Buggy python submission (verdict: Runtime Error):
import math
A, B = map(int, input().split())

GCD = math.gcd(A, B)



import collections


def primes_ordered_dict(n):
    #
    prime_list = []
    non_prime_list = []
    number_dict = collections.OrderedDict(
        ((i, None) for i in range(n + 1)))
    #
    del number_dict[0]
    del number_dict[1]
    while True:
        # get prime
        prime, _ = number_dict.popitem(False)
        if A % prime == 0 and B % prime == 0:
            prime_list.append(prime)
        # break
        if not (prime * prime <= n):
            break
        # get non primes
        non_prime_list.append(prime * prime)
        for k in number_dict:
            if prime * k <= n:
                non_prime_list.append(prime * k)
            else:
                break
        # delete non primes
        for non_prime in non_prime_list:
            del number_dict[non_prime]
        non_prime_list.clear()

    # add rest of numbers as prime
    prime_list.extend(
        [prime for prime, _ in number_dict.items() if A % prime == 0 and B % prime == 0])

    return prime_list

if GCD == 1:
    print(1)
else:
    print(len(primes_ordered_dict(GCD))+1)

Fixed submission:
import collections
import math

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


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



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

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

    return True

A_div = set(make_divisors(A))
B_div = set(make_divisors(B))
common_div = (A_div & B_div)

cnt = 1
for c in common_div:
    if is_prime(c):
        cnt += 1

print(cnt)

Buggy python submission (verdict: Runtime Error):
import math
A, B = map(int, input().split())

GCD = math.gcd(A, B)



def primes_dict(n):
    #
    prime_list = []
    non_prime_list = []
    k_list = []
    number_dict = {
        i: None for i in reversed(range(n + 1))}
    #
    del number_dict[0]
    del number_dict[1]
    while True:
        # get prime
        prime, _ = number_dict.popitem()
        if A % prime == 0 and B % prime == 0:
            prime_list.append(prime)
        if prime * prime > n:
            break

        # get non primes
        non_prime_list.append(prime * prime)
        while True:
            k, _ = number_dict.popitem()
            k_list.append(k)
            if prime * k > n:
                break
            non_prime_list.append(prime * k)

        while k_list:
            number_dict[k_list.pop()] = None

        # delete non prime
        while non_prime_list:
            del number_dict[non_prime_list.pop()]

    while number_dict:
        prime, _ = number_dict.popitem()
        if A % prime == 0 and B % prime == 0:
            prime_list.append(prime)

    return prime_list

if GCD == 1:
    print(1)
else:
    print(len(primes_dict(GCD))+1)

Fixed submission:
import collections
import math

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


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



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

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

    return True

A_div = set(make_divisors(A))
B_div = set(make_divisors(B))
common_div = (A_div & B_div)

cnt = 1
for c in common_div:
    if is_prime(c):
        cnt += 1

print(cnt)

Buggy python submission (verdict: Runtime Error):
import math
A, B = map(int, input().split())

GCD = math.gcd(A, B)



def primes_dict(n):
    #
    prime_list = []
    non_prime_list = []
    k_list = []
    number_dict = {
        i: None for i in reversed(range(n + 1))}
    #
    del number_dict[0]
    del number_dict[1]
    while True:
        # get prime
        prime, _ = number_dict.popitem()
        if A % prime == 0 and B % prime == 0:
            prime_list.append(prime)
        if prime * prime > n:
            break

        # get non primes
        non_prime_list.append(prime * prime)
        while True:
            k, _ = number_dict.popitem()
            k_list.append(k)
            if prime * k > n:
                break
            non_prime_list.append(prime * k)

        while k_list:
            number_dict[k_list.pop()] = None

        # delete non prime
        while non_prime_list:
            del number_dict[non_prime_list.pop()]

    while number_dict:
        prime, _ = number_dict.popitem()
        if A % prime == 0 and B % prime == 0:
            prime_list.append(prime)

    return prime_list

if GCD == 1:
    print(1)
else:
    print(len(primes_dict(GCD))+1)

Fixed submission:
import collections
import math

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


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



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

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

    return True

A_div = set(make_divisors(A))
B_div = set(make_divisors(B))
common_div = (A_div & B_div)

cnt = 1
for c in common_div:
    if is_prime(c):
        cnt += 1

print(cnt)