(Perfect Numbers) A positive integer is called a perfect number if it is equal to the sum of all of its positive divisors, excluding itself.  For example, 6 is the first perfect number because 6=3+2+1. The next is 28=14+7+4+2+1. There are four perfect numbers less than 10000. Write a program to find all these four numbers.

PerfectNumbers.java

/**
 * The perfect numbers less than 10000.
 */

public class PerfectNumbers {

    public static void main(String[] args) {

    	int number = 1;
    	int sum,divisor,result;
    	String perfect = "";

    	// (START) The first way (With while loop).
    		while(number<=10000){

    			sum = 0; // reset sum.
    			divisor=1;	// reset divisor.

    				while(divisor<=number/2){

    					result = number%divisor;

    						if(result==0){   						
    							sum+=divisor;	
    						}

    					divisor++;

    				} // while loop end. divisor<=number/2

    			if(sum==number){

    				perfect += " "+number;

    			}

    			number++;

    		} // while loop end. number<=10000
    	// (END) The first way (With while loop).

		// (START) The second way (With for loop).
    		/* 	
    		 	for(;number<=10000;number++){

    				sum = 0;

	    				for(divisor=1;divisor<=number/2;divisor++){

	    					result = number%divisor;

	    					if(result==0){   						
	    						sum=sum+divisor;	
	    					}	
	    				}

    				if(sum==number){

    					perfect += " "+number;

    				}
    			} 
    		*/
    	// (END) The second way (With for loop).	

			// Print perfect numbers.
    		System.out.print("The perfect numbers less than 10000 are"+perfect+".");

    } // End of main method.
} // End of class.