//Factor.cpp
//Copyright (C) 1999 Joseph Tucek
//Factors numbers using an optimized trial-division method.
#include <iostream.h>
#include <fstream.h>
#include <math.h>

void Factor(unsigned long N, unsigned long i);
ofstream Out;

int main(){
    cout << "Factor" << endl;
    cout << "Copyright (C) 1999 Joseph Tucek" << endl;
    cout << "Factors numbers using an optimized trial-division method." << endl;
    cout << endl;
    cout << "Results will be stored in out.txt" << endl;
	Out.open("out.txt");
    unsigned long i;
    cout << "Start at? ";
    cin >> i;
    unsigned long stop;
    cout << "Stop at? ";
    cin >> stop;
    for(; i>0 && i<=stop; i++){
		cout << i << " = ";
		Out << i << " = ";
		Factor(i, 2);
		cout << endl;
		Out << endl;
	}
	Out.close();
	return 0;
}

void Factor(unsigned long N, unsigned long i){
	if(N==1)
		return;
    unsigned long RootN=(unsigned long int)sqrt(N)+1;
	while(i<=RootN){
		if(!(N%i)){
			cout << i << " ";
			Out << i << " ";
			break;
		}
		i++;
	}
    if(!(i<=RootN)){
        cout << N << " ";
        Out << N << " ";
        return;
    }
	Factor(N/i, i);
}