Problem 3

/**
 *
 * @author Mat
 */
package problem.pkg3;

import java.math.BigInteger;

public class Problem3 {

    public static void main(String[] args) {
        BigInteger number = new BigInteger("600851475143");
        final int START_NUMBER = 10000;

        for(BigInteger i = BigInteger.valueOf(START_NUMBER);
                i.compareTo(BigInteger.ONE) > 0 ;i = i.subtract(BigInteger.ONE))
        {
            // is i a prime number?
            if(i.isProbablePrime(1)){
                // if yes then does it divide into the number?
                if(number.mod(i) == BigInteger.ZERO){
                    // if yes say the number
                    System.out.println("Divided by: " + i.toString());
                    // and divide it agaisnt the number
                    System.out.println("Number is now: " + (number = number.divide(i)));
                }
            }
        }
    }
}
/* output
 * Divided by: 6857
 * Number is now: 87625999
 * Divided by: 1471
 * Number is now: 59569
 * Divided by: 839
 * Number is now: 71
 * Divided by: 71
 * Number is now: 1
 */