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.
