Buggy python submission (verdict: Runtime Error):
# coding: utf-8

import sys
import math
import collections
import itertools
import bisect
INF = 10 ** 13
MOD = 10 ** 9 + 7
def input() : return sys.stdin.readline().strip()
def lcm(x, y) : return (x * y) // math.gcd(x, y)
def I() : return int(input())
def LI() : return [int(x) for x in input().split()]
def RI(N) : return [int(input()) for _ in range(N)]
def LRI(N) : return [[int(x) for x in input().split()] for _ in range(N)]
def LS() : return input().split()
def RS(N) : return [input() for _ in range(N)]
def LRS(N) : return [input().split() for _ in range(N)]
def PL(L) : print(*L, sep="\n")
def YesNo(B) : print("Yes" if B else "No")
def YESNO(B) : print("YES" if B else "NO")

def prime_factorize(N):
    res = []
    for i in range(2, int(math.sqrt(N)) + 1):
        if N % i != 0:
            continue

        num = 0
        while N % i == 0:
            N //= i
            num += 1
        
        res.append([i, num])

    if N != 1:
        res.append([N, 1])

    return res

A, B = LI()

g = math.gcd(A, B)
pf = prime_factorize(g)

print(len(pf) + 1)


Fixed submission:
# coding: utf-8

import sys
import math
import collections
import itertools
import bisect
INF = 10 ** 13
MOD = 10 ** 9 + 7
def input() : return sys.stdin.readline().strip()
def gcd(x, y) : return x if y == 0 else gcd(y, x%y)
def lcm(x, y) : return (x * y) // gcd(x, y)
def I() : return int(input())
def LI() : return [int(x) for x in input().split()]
def RI(N) : return [int(input()) for _ in range(N)]
def LRI(N) : return [[int(x) for x in input().split()] for _ in range(N)]
def LS() : return input().split()
def RS(N) : return [input() for _ in range(N)]
def LRS(N) : return [input().split() for _ in range(N)]
def PL(L) : print(*L, sep="\n")
def YesNo(B) : print("Yes" if B else "No")
def YESNO(B) : print("YES" if B else "NO")

def prime_factorize(N):
    res = []
    for i in range(2, int(math.sqrt(N)) + 1):
        if N % i != 0:
            continue

        num = 0
        while N % i == 0:
            N //= i
            num += 1
        
        res.append([i, num])

    if N != 1:
        res.append([N, 1])

    return res

A, B = LI()

g = gcd(A, B)
pf = prime_factorize(g)

print(len(pf) + 1)

Buggy python submission (verdict: Runtime Error):
# coding: utf-8

import sys
import math
import collections
import itertools
from inspect import currentframe
INF = 10 ** 10
MOD = 10 ** 9 + 7
def input() : return sys.stdin.readline().strip()
def gcd(x, y) : return y if x % y == 0 else gcd(y, x % y)
def lcm(x, y) : return (x * y) // gcd(x, y)
def I() : return int(input())
def MI() : return map(int, input().split())
def LI() : return [int(x) for x in input().split()]
def RI(N) : return [int(input()) for _ in range(N)]
def LRI(N) : return [[int(x) for x in input().split()] for _ in range(N)]
def chkprint(*args) : names = {id(v):k for k,v in currentframe().f_back.f_locals.items()}; print(', '.join(names.get(id(arg),'???')+' = '+repr(arg) for arg in args))

A, B = MI()
gcd_ab = gcd(A, B)

prime = [True] * (gcd_ab + 1)
prime[0] = False
ans = 0

for i in range(2, gcd_ab + 1):
    if A % i == 0 and B % i == 0:
        for j in range(i * 2, gcd_ab + 1, i):
            prime[j] = False

for i, p in enumerate(prime):
    if p and A % i == 0 and B % i == 0:
        ans += 1

print(ans)

Fixed submission:
# coding: utf-8

import sys
import math
import collections
import itertools
import bisect
INF = 10 ** 13
MOD = 10 ** 9 + 7
def input() : return sys.stdin.readline().strip()
def gcd(x, y) : return x if y == 0 else gcd(y, x%y)
def lcm(x, y) : return (x * y) // gcd(x, y)
def I() : return int(input())
def LI() : return [int(x) for x in input().split()]
def RI(N) : return [int(input()) for _ in range(N)]
def LRI(N) : return [[int(x) for x in input().split()] for _ in range(N)]
def LS() : return input().split()
def RS(N) : return [input() for _ in range(N)]
def LRS(N) : return [input().split() for _ in range(N)]
def PL(L) : print(*L, sep="\n")
def YesNo(B) : print("Yes" if B else "No")
def YESNO(B) : print("YES" if B else "NO")

def prime_factorize(N):
    res = []
    for i in range(2, int(math.sqrt(N)) + 1):
        if N % i != 0:
            continue

        num = 0
        while N % i == 0:
            N //= i
            num += 1
        
        res.append([i, num])

    if N != 1:
        res.append([N, 1])

    return res

A, B = LI()

g = gcd(A, B)
pf = prime_factorize(g)

print(len(pf) + 1)