Buggy python submission (verdict: Time Limit Exceeded):
def gcd(a, b):
    if a > b:
        a, b = (b, a)
    while b:
        a, b = b, a % b
    return a


def cf(x1, x2):
    ret = [1]
    gcd_num = gcd(x1, x2)

    i = 2
    while i <= gcd_num:
        if gcd_num % i == 0:
            ret.append(i)
        i += 1

    return ret


def is_prime_number(num):
    if num == 1:
        return False

    i = 2
    while i*i <= num:
        if num % i == 0:
            return False
        i += 1
    return True


def main():
    a, b = map(int, input().split())
    common_divisor_list = cf(a, b)
    # print(common_divisor_list)

    count = 0
    for num in common_divisor_list:
        if is_prime_number(num):
            count += 1

    print(count + 1)


if __name__ == '__main__':
    main()


Fixed submission:
import collections


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 gcd(a, b):
    if a > b:
        a, b = (b, a)
    while b:
        a, b = b, a % b
    return a


def main():
    a, b = map(int, input().split())
    gcd_num = gcd(a, b)
    c = collections.Counter(prime_factorize(gcd_num))
    # print(prime_factorize(gcd_num))
    # cには１が含まれていないので、その分カウントを増やす
    print(len(c) + 1)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
def cf(x1, x2):
    ret = []
    for i in range(2, min(x1, x2)+1):
        if x1 % i == 0 and x2 % i == 0:
            ret.append(i)
    return ret


def is_prime_number(num):
    if num == 1:
        return False

    i = 2
    while i*i <= num:
        if num % i == 0:
            return False
        i += 1
    return True


def main():
    a, b = map(int, input().split())
    common_divisor_list = cf(a, b)

    count = 0
    for num in common_divisor_list:
        if is_prime_number(num):
            count += 1

    print(count + 1)


if __name__ == '__main__':
    main()


Fixed submission:
import collections


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 gcd(a, b):
    if a > b:
        a, b = (b, a)
    while b:
        a, b = b, a % b
    return a


def main():
    a, b = map(int, input().split())
    gcd_num = gcd(a, b)
    c = collections.Counter(prime_factorize(gcd_num))
    # print(prime_factorize(gcd_num))
    # cには１が含まれていないので、その分カウントを増やす
    print(len(c) + 1)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
def cf(x1, x2):
    ret = []
    for i in range(2, min(x1, x2)+1):
        if x1 % i == 0 and x2 % i == 0:
            ret.append(i)
    return ret


def is_prime_number(num):
    if num == 1:
        return False

    i = 2
    while i*i <= num:
        if num % i == 0:
            return False
        i += 1
    return True


def main():
    a, b = map(int, input().split())
    common_divisor_list = cf(a, b)

    count = 0
    for num in common_divisor_list:
        if is_prime_number(num):
            count += 1

    print(count + 1)


if __name__ == '__main__':
    main()


Fixed submission:
import collections


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 gcd(a, b):
    if a > b:
        a, b = (b, a)
    while b:
        a, b = b, a % b
    return a


def main():
    a, b = map(int, input().split())
    gcd_num = gcd(a, b)
    c = collections.Counter(prime_factorize(gcd_num))
    # print(prime_factorize(gcd_num))
    # cには１が含まれていないので、その分カウントを増やす
    print(len(c) + 1)


if __name__ == '__main__':
    main()

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


def cf(x1, x2):
    ret = []
    for i in range(1, min(x1, x2)+1):
        if x1 % i == 0 and x2 % i == 0:
            ret.append(i)
    return ret


def is_prime_number(num):
    if num == 1:
        return False

    i = 2
    while i*i <= num:
        if num % i == 0:
            return False
        i += 1
    return True


def check(num):
    if num == 1:
        return True
    else:
        return is_prime_number(num)


def main():
    a, b = map(int, input().split())
    common_divisor_list = cf(a, b)

    count_set = set()

    for i in range(len(common_divisor_list) - 1):
        for j in range(i+1, len(common_divisor_list)):
            if check(common_divisor_list[i]) and check(common_divisor_list[j]):
                # print(common_divisor_list[i], common_divisor_list[j])
                count_set.add(common_divisor_list[i])
                count_set.add(common_divisor_list[j])

    if len(common_divisor_list) == 1:
        count_set.add(1)

    print(len(count_set))


if __name__ == '__main__':
    main()


Fixed submission:
import collections


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 gcd(a, b):
    if a > b:
        a, b = (b, a)
    while b:
        a, b = b, a % b
    return a


def main():
    a, b = map(int, input().split())
    gcd_num = gcd(a, b)
    c = collections.Counter(prime_factorize(gcd_num))
    # print(prime_factorize(gcd_num))
    # cには１が含まれていないので、その分カウントを増やす
    print(len(c) + 1)


if __name__ == '__main__':
    main()