""" 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. """ import math def isprime(num: int) -> bool: """Returns boolean representing primality of given number num. >>> isprime(2) True >>> isprime(3) True >>> isprime(27) False >>> isprime(2999) True >>> isprime(0) Traceback (most recent call last): ... ValueError: Parameter num must be greater or equal to two. >>> isprime(1) Traceback (most recent call last): ... ValueError: Parameter num must be greater or equal to two. """ if num <= 1: raise ValueError("Parameter num must be greater or equal to two.") if num == 2: return True elif num % 2 == 0: return False for i in range(3, int(math.sqrt(num)) + 1, 2): if num % i == 0: return False return True def solution(n: int = 600851475143) -> 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.") max_number = 0 if isprime(n): return n while n % 2 == 0: n //= 2 if isprime(n): return n for i in range(3, int(math.sqrt(n)) + 1, 2): if n % i == 0: if isprime(n / i): max_number = n / i break elif isprime(i): max_number = i return max_number if __name__ == "__main__": print(solution(int(input().strip())))