from math import gcd


def common_prime_divisors(a: list[int], b: list[int]) -> int:
    def remove_common_prime_divisors(n: int, m: int) -> int:
        while n != 1:
            d = gcd(n, m)
            if d == 1:
                break
            n //= d
        return n

    counter = 0
    for x, y in zip(a, b):
        d = gcd(x, y)

        x = remove_common_prime_divisors(x, d)
        if x != 1:
            continue

        y = remove_common_prime_divisors(y, d)
        if y == 1:
            counter += 1

    return counter