ISC Practicals and Theory - Armstrong Number

An Armstrong number is a number that equals the sum of its own digits, each raised to the power of the number of digits. This program accepts a number, counts its digits, adds up the powers and compares the sum with the number, all inside main.

Definition

A number $N$ with $k$ digits is an Armstrong number if the sum of the $k$-th powers of its digits is equal to $N$.

• $153$ has 3 digits: $1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153$. So 153 is an Armstrong number.
• $125$ has 3 digits: $1^3 + 2^3 + 5^3 = 1 + 8 + 125 = 134$, which is not $125$. So 125 is not an Armstrong number.

Algorithm

1. Accept the number n using Scanner.
2. If n <= 0, display an invalid input message and stop.
3. Count the digits of n:
   • Copy n to temp and set digits = 0.
   • While temp > 0, increase digits by 1 and do temp = temp / 10.
4. Copy n to temp again and set sum = 0.
5. While temp > 0:
   • Extract the last digit: d = temp % 10.
   • Find $d^{digits}$ in p by multiplying p by d a total of digits times, using a for loop.
   • Add p to sum.
   • Remove the last digit: temp = temp / 10.
6. If sum == n, display that it is an Armstrong number, otherwise display that it is not.

Program

The whole logic is written in the main method of class Armstrong.

import java.util.Scanner;
public class Armstrong
{
    public static void main(String args[])
    {
        Scanner sc = new Scanner(System.in);
        System.out.print("Enter a number: ");
        int n = sc.nextInt();
        if (n <= 0)
        {
            System.out.println("Invalid input. Enter a positive number.");
        }
        else
        {
            int temp = n, digits = 0;
            while (temp > 0)
            {
                digits++;
                temp = temp / 10;
            }
            temp = n;
            int sum = 0;
            while (temp > 0)
            {
                int d = temp % 10;
                int p = 1;
                for (int i = 1; i <= digits; i++)
                {
                    p = p * d;
                }
                sum = sum + p;
                temp = temp / 10;
            }
            if (sum == n)
                System.out.println(n + " is an Armstrong number.");
            else
                System.out.println(n + " is not an Armstrong number.");
        }
    }
}

Variable description table

Sample input and output

Enter a number: 153
153 is an Armstrong number.

Enter a number: 125
125 is not an Armstrong number.

Enter a number: -5
Invalid input. Enter a positive number.

Dry run

Take n = 153. The first loop counts the digits, so digits = 3. The second loop then runs with temp = 153 and sum = 0.

The loop stops as temp is 0. Since sum (153) is equal to n (153), the program displays that 153 is an Armstrong number.

Variations

1. Armstrong numbers in a range "Accept two numbers m and n and display all the Armstrong numbers between m and n."
2. Three-digit Armstrong numbers "Display all the Armstrong numbers from 100 to 999."
3. Armstrong number with a method "Write a class with a method that checks whether a number is an Armstrong number and returns true or false."