#include "cpp_headers/fcpp.hh"

int main() {
    int n = enter_int("Please enter a natural number: ");
    // search smallest factor, start with smallest possible: 2
    int k=2;
    // go until sqrt(n)
    while (k <= sqrt(n)) {
        printf("searching for dividers for %d, checking %d\n", n, k);
        // k is factor of n
        if (n % k == 0) {
            // print out the factor k
            print(k);
            // reset n to the quotient
            n = n / k;
            printf("found %d, setting n=%d\n", k, n);
            // restart at k=2
            k = 2;
        } else {
            // if k is not a factor, check next one
            k++;
        }
    }
    // n is the last prime factor of the original input number
    print(n);
}