import java.util.Scanner;

/* Java class that includes a method that, given a positive integer, prints
** its prime factorization.
** A main method is included for testing purposes.
*/
public class PrimeFactorize_F22 {

   /* Prints the prime factorization of the given integer, which is assumed
   ** to be positive.  For example, in response to 3900, what will be printed
   ** is 2 2 3 5 5 13
   */
   public static void printFactors(int n) {
      int candFactor = 2;   // candidate 
      while ( n != 1 ) {
         if (n % candFactor == 0) {  // candFactor divides into n
            System.out.print(candFactor + " ");
            n = n / candFactor;
         }
         else {
            candFactor = candFactor + 1;  //
         }
      }
      System.out.println();
   }


   public static void main(String[] args) {
      System.out.println("Welcome to the Prime Factorization program.");
      Scanner input = new Scanner(System.in);
      boolean keepGoing = true;
      while (keepGoing) {
         System.out.print("\nEnter an integer (negative to quit): ");
         int number = input.nextInt();
         if (number <= 0) { keepGoing = false; }
         else { printFactors(number); }
      }
      System.out.println("Goodbye.");
   }
}