def divisors(number, primes):
    """Finds number of divisors of a number using prime factorization."""
    prime_factors_pow = []
    if number < 2:
        prime_factors_pow.append(0)
    for p in primes:
        if p > number:
            break
        n = 0
        while number % p == 0:
            n += 1
            number //= p
        prime_factors_pow.append(n)
    num_divisors = 1
    for k in prime_factors_pow:
        num_divisors *= k + 1
    return num_divisors