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 main():
    a,b=map(lambda x: set(prime_factorize(int(x))),input().split())
    print(len(a&b)+1)

@lru_cache(maxsize=None)
def primes(n:int) -> list:
    
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n**0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    return [i for i in range(n + 1) if is_prime[i]]


@lru_cache(maxsize=None)
def is_prime(n: int) -> bool:
    
    if n == 1:
        return False
    elif n == 2:
        return True
    elif n % 2 == 0:
        return False
    
    for i in range(3, int(n**0.5)+1, 2):
        if n % i == 0:
            return False
    return True


@lru_cache(maxsize=None)
def prime_factorize(n: int) -> list:
    
    arr = []
    
    while n % 2 == 0:
        arr.append(2)
        n //= 2
    
    for f in primes(int(n**0.5)):
        while n % f == 0:
            arr.append(f)
            n //= f
    if n != 1:
        arr.append(n)
    return arr


def make_divisors(n: int) -> list:
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]
        
if __name__ == "__main__":
    main()

from functools import lru_cache

def main():
    a,b=map(lambda x: set(prime_factorize(int(x))),input().split())
    print(len(a&b)+1)

@lru_cache(maxsize=None)
def primes(n:int) -> list:
    
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n**0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    return [i for i in range(n + 1) if is_prime[i]]


@lru_cache(maxsize=None)
def is_prime(n: int) -> bool:
    
    if n == 1:
        return False
    elif n == 2:
        return True
    elif n % 2 == 0:
        return False
    
    for i in range(3, int(n**0.5)+1, 2):
        if n % i == 0:
            return False
    return True


@lru_cache(maxsize=None)
def prime_factorize(n: int) -> list:
    
    arr = []
    
    while n % 2 == 0:
        arr.append(2)
        n //= 2
    
    for f in primes(int(n**0.5)):
        while n % f == 0:
            arr.append(f)
            n //= f
    if n != 1:
        arr.append(n)
    return arr


def make_divisors(n: int) -> list:
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]
        
if __name__ == "__main__":
    main()

Verdicts: Runtime Error

Accepted