Buggy python submission (verdict: Time Limit Exceeded):
a,b = map(int,input().split())
import fractions
def disjoint_cf(x1,x2):
    cf=[]
    for i in range(2,min(x1,x2)+1):
        if x1 % i == 0 and x2 % i == 0:
            for c in cf:
                if fractions.gcd(c,i) != 1:
                    break
            else:
                cf.append(i)
                continue
    return cf

cf = disjoint_cf(a,b)
print(len(cf) + 1)


Fixed submission:
a,b = map(int,input().split())
import fractions
import collections
import copy
def prime_factorization(n):
    a = [1]
    n1 = copy.deepcopy(n)
    while n % 2 == 0:
        n //= 2
    if n1 != n:
        a.append(2)
    f = 3
    while f * f <= n:
        if n % f == 0:
            n //= f
            if a[-1] != f:
                a.append(f)
        else:
            f += 2
    if a[-1] != n and n != 1:
        a.append(n)
    return a
print(len(prime_factorization(fractions.gcd(a,b))))

Buggy python submission (verdict: Time Limit Exceeded):
a,b = map(int,input().split())
import math
def cf(x1,x2):
    cf=[]
    for i in range(2,min(x1,x2)+1):
        if x1 % i == 0 and x2 % i == 0:
            cf.append(i)
    return cf

cf = cf(a,b)
for c in cf:
    cf = [i for i in cf if i%c != 0 or i == c]
print(len(cf) + 1)


Fixed submission:
a,b = map(int,input().split())
import fractions
import collections
import copy
def prime_factorization(n):
    a = [1]
    n1 = copy.deepcopy(n)
    while n % 2 == 0:
        n //= 2
    if n1 != n:
        a.append(2)
    f = 3
    while f * f <= n:
        if n % f == 0:
            n //= f
            if a[-1] != f:
                a.append(f)
        else:
            f += 2
    if a[-1] != n and n != 1:
        a.append(n)
    return a
print(len(prime_factorization(fractions.gcd(a,b))))

Buggy python submission (verdict: Time Limit Exceeded):
a,b = map(int,input().split())
import math
def cf(x1,x2):
    cf=[]
    for i in range(2,min(x1,x2)+1):
        if x1 % i == 0 and x2 % i == 0 and is_prime(i) == True:
            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

cf = cf(a,b)
print(len(cf) + 1)


Fixed submission:
a,b = map(int,input().split())
import fractions
import collections
import copy
def prime_factorization(n):
    a = [1]
    n1 = copy.deepcopy(n)
    while n % 2 == 0:
        n //= 2
    if n1 != n:
        a.append(2)
    f = 3
    while f * f <= n:
        if n % f == 0:
            n //= f
            if a[-1] != f:
                a.append(f)
        else:
            f += 2
    if a[-1] != n and n != 1:
        a.append(n)
    return a
print(len(prime_factorization(fractions.gcd(a,b))))

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

import math
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

cf = cf(a,b)
ans = 1
for c in cf:
    if is_prime(c) == True:
        ans += 1
        cf = [i for i in cf if i % c != 0]
print(ans)


Fixed submission:
a,b = map(int,input().split())
import fractions
import collections
import copy
def prime_factorization(n):
    a = [1]
    n1 = copy.deepcopy(n)
    while n % 2 == 0:
        n //= 2
    if n1 != n:
        a.append(2)
    f = 3
    while f * f <= n:
        if n % f == 0:
            n //= f
            if a[-1] != f:
                a.append(f)
        else:
            f += 2
    if a[-1] != n and n != 1:
        a.append(n)
    return a
print(len(prime_factorization(fractions.gcd(a,b))))