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"""

Project Euler Problem 3: https://projecteuler.net/problem=3

Largest prime factor

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143?

References:

- https://en.wikipedia.org/wiki/Prime_number#Unique_factorization

"""

def solution(n: int = 600851475143) -> int:

"""

Returns the largest prime factor of a given number n.

>>> solution(13195)

>>> solution(10)

>>> solution(17)

>>> solution(3.4)

>>> solution(0)

Traceback (most recent call last):

...

ValueError: Parameter n must be greater than or equal to one.

>>> solution(-17)

Traceback (most recent call last):

...

ValueError: Parameter n must be greater than or equal to one.

>>> solution([])

Traceback (most recent call last):

...

TypeError: Parameter n must be int or castable to int.

>>> solution("asd")

Traceback (most recent call last):

...

TypeError: Parameter n must be int or castable to int.

"""

try:

n = int(n)

except (TypeError, ValueError):

raise TypeError("Parameter n must be int or castable to int.")

if n <= 0:

raise ValueError("Parameter n must be greater than or equal to one.")

prime = 1

i = 2

while i * i <= n:

while n % i == 0:

prime = i

n //= i

i += 1

if n > 1:

prime = n

return int(prime)

if __name__ == "__main__":

print(f"{solution() = }")

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