HARSHAD NUMBER / NIVEN NUMBER

HARSHAD NUMBER (or) NIVEN NUMBER:

In recreational mathematics, a harshad number (or Niven number) in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base n are also known as n-harshad (or n-Niven) numbers. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The term “Niven number” arose from a paper delivered by Ivan M. Niven at a conference on number theory in 1977. All integers between zero and n are n-harshad numbers.

Here some niven numbers are given they are:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 108, 110, 111, 112, 114, 117, 120, 126, 132, 133, 135, 140, 144, 150, 152, 153, 156, 162, 171, 180, 190, 192, 195, 198, 200, 201, 204

Example:

Let’s take the number 126. First, we must find the sum of the digits.

1 + 2 + 6 = 9

Next, we try to divide 126 by 9. And we find…

126 ÷ 9 = 14

There it is. 14 and no remainder; or put another way: 9 is a factor of 126 because

126 = 9 × 14

/*Java program to find given number is Harshad number/ niven number or not*/

import java.util.*;

class HarshadNumber

{

    public static void main(String args[])

    {

        Scanner sc = new Scanner(System.in);

         

        System.out.print("Enter a number : ");

        int n = sc.nextInt();

        int c = n, d, sum = 0;

         

        //finding sum of digits

        while(c>0)

        {

            d = c%10;

            sum = sum + d;

            c = c/10;

        }

         

        if(n%sum == 0)

            System.out.println(n+" is a Harshad Number.");

        else

            System.out.println(n+" is not a Harshad Number.");      

    }

}

OUTPUT:

Enter a number : 123

123 is not a Harshad Number

Enter a number : 6

6 is a Harshad Number.