It is a well-known mathematical fact that every integer greater than or equal to

ID: 3677366 • Letter: I

Question

It is a well-known mathematical fact that every integer greater than or equal to 2 has a unique factorization into prime numbers. For example:

40 = 2 * 2 * 2 * 5

58 = 2 * 29

9 = 3 * 3

30 = 2 * 3 * 5

100 = 2 * 2 * 5 * 5

Write a recursive function:

void printPrimeFactorization(int n, bool firstcall);

that prints out the prime factorization of the number n. (You will need to figure out for yourself the purpose of the boolean argument firstcall.)

For example, if n == 40, it should print out:

The prime factorization of 40 is 2 * 2 * 2 * 5.

also, our professor ask us to write a loop to find the smallest integer greater than or equal to 2 that divides n,

then print out this integer and call the function recursively on n/k

Explanation / Answer

PrimeFactors.java

package org.students;

import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

class PrimeFactors {

   public static void main(String args[]) {
       int n=0,k=0;
       while (true) {
           ArrayList<Integer> al = new ArrayList();
           System.out.print("Enter a Number : ");
           Scanner sc = new Scanner(System.in);
           n= sc.nextInt();
k=n;
           System.out.print("The Prime Factors of " + n + " are : ");

int i = 2;

           while (n > 1) {
               if (n % i == 0) {
                   System.out.print(i + " ");
                   n = n / i;

                   al.add(i);
               } // end of if
               else
                   i++;
           }// end of while
           int fmin = al.get(0);

           for (Integer x : al) {
               if (x < fmin) {
                   fmin = x;
               }
           }
           System.out.println(" ");
           System.out.println("Smallest Prime Integer that divides "+k+" is :"+ fmin);

           System.out.print(" Do You want to continue(Y/N):");
           char c = sc.next(".").charAt(0);
           if (c == 'Y' || c == 'y') {
               continue;
           }
           System.out.println("* Program Exit *");
           break;

}// end of while(true)

}

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