Problem statement

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

What is the largest prime factor of the number 600851475143 ?


This one will have to be solved using a loop and just checking if each prime divides. There is no known equation to find primes at certain positions like how we found the $n$th Fibonacci number in problem 2


We can use the standard prime factorisation approach of repeatedly dividing by successively higher primes, starting with two. We can limit our divisor to $\sqrt{target}$ as there can't be two prime factors larger than the square root. By the time we get to $\sqrt{target}$ the dividend must already be the largest prime factor.

#include <math.h>
#include <stdio.h>

long target = 600851475143;

int main()
	int i = 2;
	while (pow(i, 2) < target) {
		while (target % i == 0) {
			target = target / i;
	printf("%ld", target);