In math, a perfect number is a positive whole number that is equal to the sum of all its positive divisors, except itself. For example, the divisors of 6 are 1, 2, and 3 (excluding 6), and when we add them: 1 + 2 + 3 = 6. So, 6 is a perfect number. Other examples include 28, 496, and 8128.

Java is a widely-used, object-oriented programming language first developed by Sun Microsystems in 1995. Now owned by Oracle, Java runs on over 3 billion devices and supports many operating systems like Windows, macOS, and Linux.

In this article, we’ll explore how to check for perfect numbers using Java. You will learn how to write simple Java programs to check whether a number is perfect or not. We’ll also write a program to find all perfect numbers within a given range.

What is a Perfect Number in Java?

In Java, a number is called a perfect number if the sum of all its positive divisors, excluding the number itself, is equal to the number. For example, 28 is a perfect number. The divisors of 28 are 1, 2, 4, 7, 14, and 28. If we leave out 28 and add the rest: 1 + 2 + 4 + 7 + 14 = 28. Since the sum is equal to the number itself, 28 is a perfect number. While writing a Java program, we use this rule to check whether a number is perfect or not.

Example of a Perfect Number:

Let’s take the number \(496\) and check if it is a perfect number or not.

First, find the factors of \(496\), i.e. \(1\), \(2\), \(4\), \(8\), \(16\), \(31\), \(62\), \(124\), and \(248\).

Then find the sum of factors, i.e., \(1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496\).

Now, 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.

Here are a few more examples of perfect numbers:

Steps to Find Perfect Number in Java

Follow the below steps to find the perfect number in Java:

Step 1: Read or initialize a number (\(n\)).

Step 2: Declare a variable (\(s\)) for storing sum.

Step 3: Find the factors of the given number (\(n\)) by using a loop (for or while).

Step 4: Calculate the sum of factors and store it in a variable \(s\).

Step 5: 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 to find the perfect numbers.

Perfect Number in Java Programs

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

• Using while loop
• Using static method
• Using recursion

Using while Loop:

The program to find the perfect numbers in Java using while loop is given below:

import java.util.Scanner;

public class PerfectNumberExample

{

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: \(6\)

\(6\) is a perfect number.

Output 2: 

Enter the number: \(1234\)

\(1234\) is not a perfect number.

Using Static Method:

The program to find the perfect numbers in Java using static method is given below:

import java.util.Scanner;

public class PerfectNumberExample

{

/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: \(28\)

\(28\) is a perfect number.

Output 2: 

Enter the number: \(4558\)

\(4558\) is not a perfect number.

Using Recursion:

The program to find the perfect numbers in Java using recursion method is given below:

import java.util.Scanner;

public class PerfectNumberExample

{

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

PerfectNumberExample 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 not a perfect number.

The program to find and print the perfect numbers between a given range (for example, between 2 to 1000) in Java is given below:

public class PerfectNumberExample

{

/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 1000 are: “);

/loop executes until the condition n<1000 becomes false

for (int n = 2; n < 1000; 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 \(2\) and \(1000\) are:

\(6\) is a perfect number.

\(28\) is a perfect number.

\(496\) is a perfect number.

Perfect Numbers in Java Key Points to Remember

• Any number can be a perfect number in Java if the sum of its positive divisors excluding the number itself is equal to that number.
• Java is a popular programming language, created in 1995. It is owned by Oracle, and more than 3 billion devices run Java.
• There are three ways to find the perfect number in Java, i.e., using while loop, using static method, and using recursion.
• The perfect number is important because mathematically, perfect numbers give a good number theory example to the general idea of classification, i.e. all even perfects have a specific form.
• The first five perfect numbers are \(6\), \(28\), \(496\), \(8128\), and \(33550336\).

We hope that the above article is helpful for your understanding and exam preparations. Stay tuned to the Testbook App for more updates on related topics from Mathematics, and various such subjects. Also, reach out to the test series available to examine your knowledge regarding several exams.