Problem: Given are positive integers A and B.  Let us choose some number of positive common divisors of A and B.  Here, any two of the chosen divisors must be coprime.  At most, how many divisors can we choose?  Definition of common divisor  An integer d is said to be a common divisor of integers x and y when d divides both x and y.  Definition of being coprime  Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.  Definition of dividing  An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.

Submission attempts (in order):
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a
 

import math
def sieve_of_eratosthenes2(target):
    dest = int(math.sqrt(target))
    target_list = [i for i in range(2, dest+1) if target%i==0]
    prime_num = 0
 
    while True:
        num_min = min(target_list)
        if num_min > dest:
            prime_num += len(target_list)
            break
        prime_num += 1        
        target_list = [i for i in target_list if i%num_min!=0]
        if target_list==[]:
            break
 
    return prime_num   
 
a, b = map(int, input().split())
gcd = xgcd(a, b)
if gcd == 1:
    print(1)
else:
    ans = sieve_of_eratosthenes2(gcd)    
    print(ans+1)

def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a


import math
def sieve_of_eratosthenes2(target):
    dest = math.ceil(math.sqrt(target))
    target_list = [i for i in range(2, dest//2+1) if target%i==0]
    prime_num = 0
 
    while True:
        num_min = target_list[0]
        if num_min > dest:
            prime_num += len(target_list)
            break
        prime_num += 1        
        target_list = [i for i in target_list if i%num_min!=0]
        if target_list==[]:
            break
 
    return prime_num

import random
def is_prime(q, k=50):
    q = abs(q)
    if q == 2:
        return True
    if q < 2 or q % 2 == 0:
        return False

    d = (q - 1) >> 1
    while d & 1 == 0:
        d >>= 1
    for i in range(k):
        a = random.randint(1, q - 1)
        t = d
        y = pow(a, t, q)
        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

a, b = map(int, input().split())
gcd = xgcd(a, b)
if gcd == 1:
    print(1)
elif is_prime(gcd):
    print(2)
else:
    ans = sieve_of_eratosthenes2(gcd)    
    print(ans+1)


def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a


import random
def is_prime(q, k=50):
    q = abs(q)
    if q == 2:
        return True
    if q < 2 or q % 2 == 0:
        return False

    d = (q - 1) >> 1
    while d & 1 == 0:
        d >>= 1
    for i in range(k):
        a = random.randint(1, q - 1)
        t = d
        y = pow(a, t, q)
        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 prime_num(target):
    ra = 2
    prime = 0
    while target>1:
        if target%ra == 0:
            prime += 1
            while target%ra==0:
                target = target//ra
            if is_prime(target):
                prime += 1
                break
        if ra == 2:
            ra += 1
        else:
            ra += 2
    return prime   
        
a, b = map(int, input().split())
gcd = xgcd(a, b)
if gcd == 1:
    print(1)
elif is_prime(gcd):
    print(2)
else:
    ans = prime_num(gcd)    
    print(ans+1)

Verdicts: Runtime Error

Runtime Error

Accepted