project euler problem 3 https projecteuler netproblem3 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 orgwikiprimenumberuniquefactorization checks to see if a number is a prime in osqrtn a number is prime if it has exactly two factors 1 and itself returns boolean representing primality of given number i e if the result is true then the number is indeed prime else it is not isprime2 true isprime3 true isprime27 false isprime2999 true isprime0 false isprime1 false 2 and 3 are primes negatives 0 1 all even numbers all multiples of 3 are not primes all primes number are in format of 6k 1 returns the largest prime factor of a given number n solution13195 29 solution10 5 solution17 17 solution3 4 3 solution0 traceback most recent call last valueerror parameter n must be greater than or equal to one solution17 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 solutionasd traceback most recent call last typeerror parameter n must be int or castable to int checks to see if a number is a prime in o sqrt n a number is prime if it has exactly two factors 1 and itself returns boolean representing primality of given number i e if the result is true then the number is indeed prime else it is not is_prime 2 true is_prime 3 true is_prime 27 false is_prime 2999 true is_prime 0 false is_prime 1 false 2 and 3 are primes negatives 0 1 all even numbers all multiples of 3 are not primes all primes number are in format of 6k 1 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 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
import math


def is_prime(number: int) -> bool:
    

    if 1 < number < 4:
        
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        
        return False

    
    for i in range(5, int(math.sqrt(number) + 1), 6):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True


def solution(n: int = 600851475143) -> 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.")
    max_number = 0
    if is_prime(n):
        return n
    while n % 2 == 0:
        n //= 2
    if is_prime(n):
        return n
    for i in range(3, int(math.sqrt(n)) + 1, 2):
        if n % i == 0:
            if is_prime(n // i):
                max_number = n // i
                break
            elif is_prime(i):
                max_number = i
    return max_number


if __name__ == "__main__":
    print(f"{solution() = }")