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


A, B = [int(str) for str in input().split()]

def gcd(a,b):
  while b!=0:
    a,b=b,a%b
  return a

def is_prime(q,k=2):
    q = abs(q)
    #計算するまでもなく判定できるものははじく
    if q == 2: return True
    if q < 2 or q&1 == 0: return False

    #n-1=2^s*dとし(但しaは整数、dは奇数)、dを求める
    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1
    
    #判定をk回繰り返す
    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        #[0,s-1]の範囲すべてをチェック
        while t != q-1 and y != 1 and y != q-1: 
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return False
    return True

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    divisors.sort()
    return divisors


prime_list = [1] + [i for i in range(1, gcd(A, B) + 1) if is_prime(i)]
print(len([i for i in prime_list if A % i == 0 and B % i == 0]))

Fixed submission:
A, B = [int(str) for str in input().split()]

def gcd(a,b):
  while b!=0:
    a,b=b,a%b
  return a


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


print(len(set(prime_factorize(gcd(A, B)))) + 1)

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


A, B = [int(str) for str in input().split()]

def gcd(a,b):
  while b!=0:
    a,b=b,a%b
  return a

def is_prime(q,k=4):
    q = abs(q)
    #計算するまでもなく判定できるものははじく
    if q == 2: return True
    if q < 2 or q&1 == 0: return False

    #n-1=2^s*dとし(但しaは整数、dは奇数)、dを求める
    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1
    
    #判定をk回繰り返す
    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        #[0,s-1]の範囲すべてをチェック
        while t != q-1 and y != 1 and y != q-1: 
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return False
    return True

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    divisors.sort()
    return divisors


prime_list = [1] + [i for i in range(1, gcd(A, B) + 1) if is_prime(i)]
print(len([i for i in prime_list if A % i == 0 and B % i == 0]))

Fixed submission:
A, B = [int(str) for str in input().split()]

def gcd(a,b):
  while b!=0:
    a,b=b,a%b
  return a


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


print(len(set(prime_factorize(gcd(A, B)))) + 1)

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


A, B = [int(str) for str in input().split()]

def gcd(a,b):
  while b!=0:
    a,b=b,a%b
  return a

def is_prime(q,k=4):
    q = abs(q)
    #計算するまでもなく判定できるものははじく
    if q == 2: return True
    if q < 2 or q&1 == 0: return False

    #n-1=2^s*dとし(但しaは整数、dは奇数)、dを求める
    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1
    
    #判定をk回繰り返す
    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        #[0,s-1]の範囲すべてをチェック
        while t != q-1 and y != 1 and y != q-1: 
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return False
    return True

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    divisors.sort()
    return divisors


if A < B:
    A, B = B, A

div_list = [i for i in make_divisors(B) if A % i == 0]
prime_list = [1] + [i for i in range(1, gcd(A, B) + 1) if is_prime(i)]
print(len([i for i in prime_list if i in div_list]))

Fixed submission:
A, B = [int(str) for str in input().split()]

def gcd(a,b):
  while b!=0:
    a,b=b,a%b
  return a


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


print(len(set(prime_factorize(gcd(A, B)))) + 1)

Buggy python submission (verdict: Runtime Error):
import random, math


A, B = [int(str) for str in input().split()]

def is_prime(q,k=4):
    q = abs(q)
    #計算するまでもなく判定できるものははじく
    if q == 2: return True
    if q < 2 or q&1 == 0: return False

    #n-1=2^s*dとし(但しaは整数、dは奇数)、dを求める
    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1
    
    #判定をk回繰り返す
    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        #[0,s-1]の範囲すべてをチェック
        while t != q-1 and y != 1 and y != q-1: 
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return False
    return True

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    divisors.sort()
    return divisors


if A < B:
    A, B = B, A

div_list = [i for i in make_divisors(B) if A % i == 0]
prime_list = [1] + [i for i in range(1, math.gcd(A, B) + 1) if is_prime(i)]
print(len([i for i in prime_list if i in div_list]))

Fixed submission:
A, B = [int(str) for str in input().split()]

def gcd(a,b):
  while b!=0:
    a,b=b,a%b
  return a


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


print(len(set(prime_factorize(gcd(A, B)))) + 1)