sol3 Algorithm

"""
Problem:
The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor
of a given number N?

e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
"""


def solution(n: int) -> int:
    """Returns the largest prime factor of a given number n.

    >>> solution(13195)
    29
    >>> solution(10)
    5
    >>> solution(17)
    17
    >>> solution(3.4)
    3
    >>> solution(0)
    Traceback (most recent call last):
        ...
    ValueError: Parameter n must be greater or equal to one.
    >>> solution(-17)
    Traceback (most recent call last):
        ...
    ValueError: Parameter n must be greater or equal to one.
    >>> solution([])
    Traceback (most recent call last):
        ...
    TypeError: Parameter n must be int or passive of cast to int.
    >>> solution("asd")
    Traceback (most recent call last):
        ...
    TypeError: Parameter n must be int or passive of cast to int.
    """
    try:
        n = int(n)
    except (TypeError, ValueError):
        raise TypeError("Parameter n must be int or passive of cast to int.")
    if n <= 0:
        raise ValueError("Parameter n must be greater or equal to one.")
    i = 2
    ans = 0
    if n == 2:
        return 2
    while n > 2:
        while n % i != 0:
            i += 1
        ans = i
        while n % i == 0:
            n = n / i
        i += 1

    return int(ans)


if __name__ == "__main__":
    # print(solution(int(input().strip())))
    import doctest

    doctest.testmod()