#!/usr/bin/python3
# -*- coding: utf-8 -*-

import sys
from typing import List


def trial_division(n: int) -> List[int]:
    """Return a list of the prime factors for a natural number."""
    # Prepare an empty list.
    factors: List[int] = []
    # The first possible factor.
    possible_factor: int = 2
    # While n still has remaining factors...
    while n > 1:
        # The remainder of n divided by f might be zero.
        if n % possible_factor == 0:
            # If so, it divides n. Add f to the list.
            factors.append(possible_factor)
            # Divide that factor out of n.
            n //= possible_factor
        # But if f is not a factor of n,
        else:
            # Add one to f and try again.
            possible_factor += 1
    # Prime factors may be repeated: 12 factors to 2, 2, 3.
    return factors


if __name__ == "__main__":
    print("Example trial division of 17: ", trial_division(17))
    print("Example trial division of 16: ", trial_division(257))
    print("Example trial division of 16: ", trial_division(16))