factoring integers

                              Factors.java

/*************************************************************************
 *  Compilation:  javac Factors.java
 *  Execution:    java Factors N
 *  
 *  Computes the prime factorization of N using brute force.
 *
 *   % java Factors 81
 *   The prime factorization of 81 is: 3 3 3 3 
 *
 *   % java Factors 168
 *   The prime factorization of 168 is: 2 2 2 3 7
 *
 *   % java Factors 4444444444
 *   The prime factorization of 4444444444 is: 2 2 11 41 271 9091 
 *
 *   % java Factors 4444444444444463
 *   The prime factorization of 4444444444444463 is: 4444444444444463
 * 
 *   % java Factors 10000001400000049
 *   The prime factorization of 10000001400000049 is: 100000007 100000007 
 *
 *   % java Factors 1000000014000000049
 *   The prime factorization of 1000000014000000049 is: 1000000007 1000000007
 *
 *   % java Factors 9201111169755555649
 *   The prime factorization of 9201111169755555649 is: 3033333343 3033333343 
 *
 *   Can use these for timing tests - biggest 3, 6, 9, 12, 15, and 18 digit primes
 *   % java Factors 997
 *   % java Factors 999983
 *   % java Factors 999999937
 *   % java Factors 999999999989
 *   % java Factors 999999999999989
 *   % java Factors 999999999999999989
 *
 *   Remarks
 *   -------
 *   - Tests i*i <= N instead of i <= N for efficiency.
 *
 *   - The last two examples still take a few minutes.
 *
 *************************************************************************/

public class Factors {

    public static void main(String[] args) { 

        // command-line argument
        long n = Long.parseLong(args[0]);

        System.out.print("The prime factorization of " + n + " is: ");

        // for each potential factor i
        for (long i = 2; i*i <= n; i++) {

            // if i is a factor of N, repeatedly divide it out
            while (n % i == 0) {
                System.out.print(i + " "); 
                n = n / i;
            }
        }

        // if biggest factor occurs only once, n > 1
        if (n > 1) System.out.println(n);
        else       System.out.println();
    }
}