Buggy python submission (verdict: Runtime Error):
import math
from collections import Counter

def read():
    return int(input())

def readmap():
    return map(int, input().split())

def readlist():
    return list(map(int, input().split()))

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

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

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


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


if __name__ == "__main__":
    a, b = readmap()
    g = math.gcd(a, b)

    c = Counter(prime_factorize(g))

    print(len(c) + 1)

Fixed submission:
import math
import fractions
from collections import Counter

def read():
    return int(input())

def readmap():
    return map(int, input().split())

def readlist():
    return list(map(int, input().split()))

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

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

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


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


if __name__ == "__main__":
    a, b = readmap()
    g = fractions.gcd(a, b)

    c = Counter(prime_factorize(g))

    print(len(c) + 1)

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


def read():
    return int(input())

def readmap():
    return map(int, input().split())

def readlist():
    return list(map(int, input().split()))

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

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

if __name__ == "__main__":
    a, b = readmap()

    lst = cf(a, b)

    ans = sum([is_prime(e) for e in lst]) + 1

    print(ans)

Fixed submission:
import math
import fractions
from collections import Counter

def read():
    return int(input())

def readmap():
    return map(int, input().split())

def readlist():
    return list(map(int, input().split()))

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

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

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


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


if __name__ == "__main__":
    a, b = readmap()
    g = fractions.gcd(a, b)

    c = Counter(prime_factorize(g))

    print(len(c) + 1)