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

unsigned long largestPrimeFactor(unsigned long n);

int main(void)
{
    unsigned long n;

    printf("please enter a number to find the largest prime factor:\n");
    scanf("%lu", &n);

    printf("\n\nThe largest prime factor is: %lu\n",
        largestPrimeFactor(n));

    return 0;
}

unsigned long largestPrimeFactor(unsigned long n)
{
    unsigned long x = (unsigned long) sqrt(n);

    while (n % x != 0)
        x--;

    // x is a factor (may be prime or composite)
    // and splits n into its largest divisions

    if (x == 1)
    {
        printf("Found a prime! %lu\n", n);
        return n;  // n is prime
    }

    unsigned long s = largestPrimeFactor(x);
    unsigned long t = largestPrimeFactor(n/x);

    return ((s > t) ? s : t); // return larger value
}