Buggy python submission (verdict: Time Limit Exceeded):
import fractions
from itertools import combinations
import heapq
def cf(x1,x2):
    cf=[1]
    for i in range(2,min(x1,x2)+1):
        if x1 % i == 0 and x2 % i == 0:
            cf.append(i)
    return cf
def compromise(x1, x2):
    f = fractions.gcd(x1, x2)
    return f == 1
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 isPrime(n):
  if n < 2:
    # 2未満は素数でない
    return False
  if n == 2:
    # 2は素数
    return True
  for p in range(2, n):
      if n % p == 0:
        # nまでの数で割り切れたら素数ではない
        return False
  # nまでの数で割り切れなかったら素数
  return True

a, b = map(int, input().split())
cfs = cf(a, b)
total = len(cfs)
for c in cfs:
    if not isPrime(c):
        total -= 1
print(total+1)

Fixed submission:
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
a, b = map(int, input().split())
apri = set(prime_factorize(a))
bpri = set(prime_factorize(b))
print(len(apri & bpri)+1)

Buggy python submission (verdict: Time Limit Exceeded):
import fractions
from itertools import combinations
def cf(x1,x2):
    cf=[1]
    for i in range(2,min(x1,x2)+1):
        if x1 % i == 0 and x2 % i == 0:
            cf.append(i)
    return cf
def compromise(x1, x2):
    f = fractions.gcd(x1, x2)
    return f == 1
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

a, b = map(int, input().split())
cfs = cf(a, b)
primes = []
for c in cfs:
    primes += prime_factorize(c)
print(len(set(primes))+1)

Fixed submission:
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
a, b = map(int, input().split())
apri = set(prime_factorize(a))
bpri = set(prime_factorize(b))
print(len(apri & bpri)+1)

Buggy python submission (verdict: Time Limit Exceeded):
import fractions
from itertools import combinations
def cf(x1,x2):
    cf=[1]
    for i in range(2,min(x1,x2)+1):
        if x1 % i == 0 and x2 % i == 0:
            cf.append(i)
    return cf
def compromise(x1, x2):
    f = fractions.gcd(x1, x2)
    return f == 1

a, b = map(int, input().split())
cfs = cf(a, b)
club = []
for i in range(len(cfs)):
    if i == 0:
        club.append(cfs[i])
    else:
        flag = True
        for c in club:
            if not compromise(cfs[i], c):
                flag = False
                break
        if flag:
            club.append(cfs[i])
print(len(club))


Fixed submission:
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
a, b = map(int, input().split())
apri = set(prime_factorize(a))
bpri = set(prime_factorize(b))
print(len(apri & bpri)+1)

Buggy python submission (verdict: Time Limit Exceeded):
import fractions
from itertools import combinations
def cf(x1,x2):
    cf=[1]
    for i in range(2,min(x1,x2)+1):
        if x1 % i == 0 and x2 % i == 0:
            cf.append(i)
    return cf
def compromise(x1, x2):
    f = fractions.gcd(x1, x2)
    return f == 1

a, b = map(int, input().split())
cfs = cf(a, b)
club = []
for i in range(len(cfs)):
    if i == 0:
        club.append(cfs[i])
    else:
        flag = True
        for c in club:
            if not compromise(cfs[i], c):
                flag = False
        if flag:
            club.append(cfs[i])
print(len(club))

Fixed submission:
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
a, b = map(int, input().split())
apri = set(prime_factorize(a))
bpri = set(prime_factorize(b))
print(len(apri & bpri)+1)