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

def cf(x, y):
    cf = [1]
    if x % 2 == 0 and y % 2 == 0:
        cf.append(2)

    for i in range(3, min(x,y)+1, 2):
        if x % i == 0 and y % i == 0:
            cf.append(i)
    return cf

def comprime(a, b):
    return fractions.gcd(a, b) == 1

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

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

y = cf(A,B)

c = [1]

for i in range(1, len(y)):
    for j in range(1,len(c)):
        if comprime(y[i], c[j]) == False:
            break
    else:
        c.append(y[i])


print(len(c))


Fixed submission:
from fractions import gcd
A,B = map(int, input().split())
g=gcd(A,B)
def prime_factorization(n):
    prime_num = []
    for i in range(2, int(n**.5)+1):
        num = 0
        while True:
            x,y = divmod(n, i)
            if y!= 0:
                break
            n = x
            num += 1
        if num>0:
            prime_num.append(i)
    if n > 1:
        prime_num.append(n)
    return prime_num
print(len(prime_factorization(g))+1)

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

def cf(x, y):
    cf = [1]
    for i in range(2, min(x,y)+1):
        if x % i == 0 and y % i == 0:
            cf.append(i)
    return cf

def comprime(a, b):
    return fractions.gcd(a, b) == 1

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

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

y = cf(A,B)

so = [1]
cnt = 1
for i in range(1,len(y)-1):
    for j in range(len(so)):
        if comprime(y[i], so[j]) == False:
            break
    else:
        cnt += 1
        so.append(y[i])

print(cnt)


Fixed submission:
from fractions import gcd
A,B = map(int, input().split())
g=gcd(A,B)
def prime_factorization(n):
    prime_num = []
    for i in range(2, int(n**.5)+1):
        num = 0
        while True:
            x,y = divmod(n, i)
            if y!= 0:
                break
            n = x
            num += 1
        if num>0:
            prime_num.append(i)
    if n > 1:
        prime_num.append(n)
    return prime_num
print(len(prime_factorization(g))+1)

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

def cf(x, y):
    cf = [1]
    for i in range(2, min(x,y)+1):
        if x % i == 0 and y % i == 0:
            cf.append(i)
    return cf

def comprime(a, b):
    return fractions.gcd(a, b) == 1

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

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

y = cf(A,B)

cnt = 0
for yi in y:
    if is_prime(yi):
        cnt += 1

print(cnt)


Fixed submission:
from fractions import gcd
A,B = map(int, input().split())
g=gcd(A,B)
def prime_factorization(n):
    prime_num = []
    for i in range(2, int(n**.5)+1):
        num = 0
        while True:
            x,y = divmod(n, i)
            if y!= 0:
                break
            n = x
            num += 1
        if num>0:
            prime_num.append(i)
    if n > 1:
        prime_num.append(n)
    return prime_num
print(len(prime_factorization(g))+1)