Perfect Number Program in Java

Perfect Number Program in Java

A perfect number is a number whose sum of all the factors, excluding the number itself, is equal to the number. For example, 28 is a perfect number. This is because all the factors of the number 28, excluding the number itself are: 1, 2, 4, 7, 14, and their sum is 1 + 2 + 4 + 7 + 14 = 28. The perfect number program in Java checks whether the given is the perfect number or not.

The steps required to find the perfect are as follows:

Step 1: Declare a variable x.

Step 2: Take input from the user and assign it to the variable x.

Step 3:  Declare another variable sumOfFactors. Assign value zero to it, i.e., sumOfFactors = 0.

Step 4: Find all the factors of x, barring x itself.

Step 5: Store the sum of all factors found in step 3, in the variable sumOfFactors.

Step 6: Compare sumOfFactors and x to check whether they are equal or not; if they are equal, the input number is perfect number; otherwise, not.

There are two ways to implement the above steps: one is iterative, and another is recursive. Let’s start with the iterative approach.

Iterative Approach

Filename: PerfectNumber.java

// importing the Scanner class
import java.util.Scanner;
public class PerfectNumber
{
public static void main(String argvs[])
{
    int x; // contains the number given by the user
    // creating an object of the Scanner class
    Scanner scr = new Scanner(System.in);
    System.out.println("Enter a number " );
    x = scr.nextInt(); // reading input from the user
    int sumOfFactors = 0; // storing the sum of the factors of the input number
    // loop for finding the factors of
    // the given number other than itself
    for(int i = 1; i <= x / 2; i++)
    {
        if(x % i == 0)
        {
            // factor found!
            // doing the summation of factors
            sumOfFactors = sumOfFactors + i;
        }
    }
    // displaying the outcome
    if(x == sumOfFactors)
    {
        System.out.println("Entered number " + x + " is a perfect number. " );
    }
    else
    {
        System.out.println("Entered number " + x + " is not a perfect number. " );       
    }
}
} 

Output 1:

 Enter a number
6
Entered number 6 is a perfect number. 

Output 2:

 Enter a number
15
Entered number 15 is not a perfect number. 

Explanation:  In the above code, we are storing the input from the user in the variable x. Then, using the Java for-loop, we are finding the factors of x. The iterations start from 1 and go till x / 2. This way, we are excluding the number x from the factors. Every number from 1 to x / 2 is checked for the factors of x. If the factor is found, that factor is added to the variable sumOfFactors. Eventually, we are checking the sumOfFactors with x and displaying the result accordingly.

Recursive Approach

Filename: PerfectNumber1.java

 // importing the Scanner class
import java.util.Scanner;
public class PerfectNumber1
{
static int sumOfFactors = 0; // storing the sum of the factors of the input number
// Method for finding and adding factors of the input number
public static void perfectNoFactors(int n, int i)
{
    // handling base case
    if(i > n / 2)
    {
        return;
    }
    if( n % i == 0 )
    {
        // factor found!
        // adding the factors of the variable sumOfFactors
        sumOfFactors = sumOfFactors + i;
    }
    // recursively searching for factors
    perfectNoFactors(n, i + 1);
}
public static void main(String argvs[])
{
    int x; // contains the number given by the user
    // creating an object of the Scanner class
    Scanner scr = new Scanner(System.in);
    System.out.println("Enter a number " );
    x = scr.nextInt(); // reading input from the user
    perfectNoFactors(x, 1); // calling the method perfectNoFactors
    // displaying the result
    if(sumOfFactors == x)
    {
        System.out.println("Entered number " + x + " is a perfect number. " );
    }
    else
    {
        System.out.println("Entered number " + x + " is not a perfect number. " );
    }
}
} 

Output1:

 Enter a number
6
Entered number 6 is a perfect number. 

Output2:

 Enter a number
7
Entered number 7 is not a perfect number. 

Explanation: Instead of Java for-loop, we have relied upon the recursive call to find the factors of x. The approach still remains the same, i.e., to check every number between 1 and x / 2 in order to get the factors of x, excluding x itself.

To find perfect numbers between 1 to 500

The following Java program displays perfect numbers present between 1 to 500.

Filename: PerfectNumber2.java

 public class PerfectNumber2
{
private static Boolean isPerfectNo(int n)
{
    // for containing sum of the factors of number n
    int sum = 0;
    //loop for finding factors till n/2
    for(int i =  1; i <= n / 2; i++)
    {
        if(n % i == 0)
        {
            // Factor found!
            // Updating sum
            sum = sum + i;
        }
    }
    Boolean isEqual;
    // checking whether n is equal to sum or not
    isEqual = (n == sum) ? true : false;
    //returning the result
    return isEqual;
}
// main method
public static void main(String argvs[])
{
    int no = 500; // till 500, we are finding the perfect numbers
    // loop for finding pefect number from 1 till 500
    for(int i = 1; i <= no; i++)
    {
        if(isPerfectNo(i)) // calling the method isPerfectNo()
        {
            // Displaying the perfect numbers from 1 to 500
            System.out.println(i + " is a prefect number");
        }
    }
}
} 

Output:

 6 is a perfect number
28 is a perfect number
496 is a perfect number 

Explanation: In the main method, the Java for-loop is iterating from 1 to 500. In each iteration, we are calling the method isPerfectNo(), whose return type is Boolean. The method takes a number (n) in its argument and checks whether that number, n, is a perfect number or not. If n is a perfect number, the method returns true; otherwise, false. For those numbers, where the method isPerfectNo() has returned false, are discarded, and the rest of the numbers are printed on the console.