Perfect Number Program in Java

In this section, we will learn what is a perfect number in Java and also create Java programs to check if the given number is perfect or not. Also, we will create a Java program for finding all the perfect numbers between the given range. The perfect number program frequently asked in Java coding tests and academics.

What is a perfect number in Java?

A number whose sum of factors (excluding the number itself) is equal to the number is called a perfect number. In other words, if the sum of positive divisors (excluding the number itself) of a number equals the number itself is called a perfect number. Let's understood it through an example.

Example of a Perfect Number

Let's take the number 496 and heck it is a perfect number or not.

First, we find the factors of 496 i.e. 1, 2, 4, 8, 16, 31, 62, 124, and 248. Let's find the sum of factors (1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 +248 = 496). We observe that the sum of factors is equal to the number itself. Hence, the number 496 is a perfect number. Similarly, we can check other numbers also.

Some other perfect numbers are 6, 8128, 33550336, 8589869056, etc.

Steps to Find Perfect Number

Read or initialize a number (n).
Declare a variable (s) for storing sum.
Find the factors of the given number (n) by using a loop (for/ while).
Calculate the sum of factors and store it in a variable s.
Compare the sum (s) with the number (n):
- If both (s and n) are equal, then the given number is a perfect number.
- Else, the number is not a perfect number.

Let's implement the above steps in a Java program.

Perfect Number Java Programs

There are the following ways to find the perfect number in Java:

Using while Loop
Using Method
Using Recursion

Using while Loop

PerfectNumberExample1.java

import java.util.Scanner;
public class PerfectNumberExample1
{
public static void main(String args[])	
{
long n, sum=0;
Scanner sc=new Scanner(System.in);	   	 
System.out.print("Enter the number: ");
n=sc.nextLong();
int i=1;
//executes until the condition becomes false
while(i <= n/2)
{
if(n % i == 0)
{
//calculates the sum of factors
Sum = sum + i;
} //end of if
//after each iteration, increments the value of variable i by 1
i++;
} //end of while
//compares sum with the number
if(sum==n)
{
//prints if sum and n are equal
System.out.println(n+" is a perfect number.");
} //end of if
else
//prints if sum and n are not equal
System.out.println(n+" is not a perfect number."); 
}
}

Output 1:

Enter the number: 28
28 is a perfect number.

Output 2:

Enter the number: 4558
4558 is not a perfect number.

Using Method

PerfectNumberExample2.java

import java.util.Scanner;
public class PerfectNumberExample2
{
//function that checks if the given number is perfect or not
static long isPerfect(long num)
{
//variable stores the sum    
long sum=0;
//executes until the condition becomes false
for(int i=1; i <= num/2; i++)
{
if(num % i == 0)
{
//calculates the sum of factors
sum=sum + i;
} //end of if
}  //end of for
//returns the sum of factors
return sum;	
} //end of method
public static void main(String args[])	
{
long number, s;
Scanner sc=new Scanner(System.in);	   	 
System.out.print("Enter the number: ");
//reads a number from the user
number=sc.nextLong();
//calling the function
s = isPerfect(number);
//compares sum with the number
if(s==number)
System.out.println(number+" is a perfect number");
else
System.out.println(number+" is not a perfect number"); 
} 
}

Output 1:

Enter the number: 6
6 is a perfect number.

Output 2:

Enter the number: 1234
1234 is not a perfect number.

Using Recursion

PerfectNumberExample3.java

import java.util.Scanner;
public class PerfectNumberExample3
{ 	
static long sum=0;	
long isPerfect(long num, int i)
{
//executes until the condition becomes false    
if(i <= num/2)
{
if(num % i ==0)
{
//calculates the sum of factors    
sum=sum + i;
}
//after each iteration, increments the value of variable i by 1
i++;
//recursively called function
isPerfect(num, i);
}
//returns the sum of factors
return sum;	
}
//driver code
public static void main(String args[])	
{
long number, s;
int i=1;
Scanner sc=new Scanner(System.in);	   	 
System.out.print("Enter the number: ");
//reads a number from the user
number=sc.nextLong();
//creating an object of the class
PerfectNumberExample3 pne=new PerfectNumberExample3( );
s = pne.isPerfect(number, i);
//compares sum with the number
if(s == number)
//prints if the s and number are equal
System.out.println(number+" is a perfect number");
else
//prints if s and number are not equal
System.out.println(number+" is not a perfect number"); 
} 
}

Output 1:

Enter the number: 8128
8128 is a perfect number.

Output 2:

Enter the number: 7866
7866 is a perfect number.

Perfect Numbers Between Given Range

The following program finds all the perfect numbers between a given range.

PerfectNumberExample3.java

public class PerfectNumberExample3
{
//function checks if the given number is perfect or not
static boolean isPerfectNumber(int num)
{
//variable stores the sum of divisors
int sum = 1;
//determines all the divisors of the given number and adds them
for (int i = 2; i * i <= num; i++)
{
if (num % i==0)
{
if(i * i != num)
sum = sum + i + num / i;
else
//calculates the sum of factors
sum = sum + i;
}  //end of if
}  //end of for
if (sum == num && num != 1)
//returns true if both conditions (above) returns true
return true;
//returns false if any condition becomes false
return false;
} //end of function
//driver code
public static void main (String args[])
{
System.out.println("Perfect Numbers between 2 to 10000 are: ");
//loop executes until the condition n<10000 becomes false
for (int n = 2; n < 10000; n++)
//calling function
if (isPerfectNumber(n))
//prints all perfect number between given range
System.out.println(n +" is a perfect number");
}
}

Output:

Perfect Numbers between 2 to 10000 are: 
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

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Perfect Number Program in Java

What is a perfect number in Java?

Example of a Perfect Number

Steps to Find Perfect Number

Perfect Number Java Programs

Using while Loop

Using Method

Using Recursion

Perfect Numbers Between Given Range

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Perfect Number Program in Java

What is a perfect number in Java?