Harshad (Or Niven) Number

Last Updated : 11 Sep, 2023

An integer number in base 10 which is divisible by the sum of its digits is said to be a Harshad Number. An n-Harshad number is an integer number divisible by the sum of its digit in base n.
Below are the first few Harshad Numbers represented in base 10:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20.........
Given a number in base 10, our task is to check if it is a Harshad Number or not.

Examples :

Input: 3
Output: 3 is a Harshad Number

Input: 18
Output: 18 is a Harshad Number

Input: 15
Output: 15 is not a Harshad Number

1. Extract all the digits from the number using the % operator and calculate the sum.
2. Check if the number is divisible by the sum.

Below is the implementation of the above idea:

C++

// C++ program to check if a number is Harshad 
// Number or not. 
#include <bits/stdc++.h> 
using namespace std; 
  
// function to check Harshad Number 
bool checkHarshad(int n) 
{ 
    // calculate sum of digits 
    int sum = 0; 
    for (int temp = n; temp > 0; temp /= 10) 
        sum += temp % 10; 
  
    // Return true if sum of digits is multiple 
    // of n 
    return (n % sum == 0); 
} 
  
// driver program to check above function 
int main() 
{ 
    checkHarshad(12) ? cout << "Yes\n" : cout << "No\n"; 
    checkHarshad(15) ? cout << "Yes\n" : cout << "No\n"; 
  
    return 0; 
}

Java

// Java program to check if a number is Harshad
// Number or not

public class GFG {
    // method to check Harshad Number
    static boolean checkHarshad(int n)
    {
        // calculate sum of digits
        int sum = 0;
        for (int temp = n; temp > 0; temp /= 10)
            sum += temp % 10;

        // Return true if sum of digits is multiple
        // of n
        return (n % sum == 0);
    }

    // Driver program to test above functions
    public static void main(String[] args)
    {
        System.out.println(checkHarshad(12) ? "Yes" : "No");
        System.out.println(checkHarshad(15) ? "Yes" : "No");
    }
}

Python3

# Python program to check 
# if a number is Harshad 
# Number or not.

def checkHarshad( n ) :
    sum = 0
    temp = n
    while temp > 0 :
        sum = sum + temp % 10
        temp = temp // 10
    # Return true if sum of
    # digits is multiple of n
    return n % sum == 0

# Driver Code
if(checkHarshad(12)) : print("Yes")
else : print ("No")

if (checkHarshad(15)) : print("Yes")
else : print ("No")
    
# This code is contributed
# by Nikita Tiwari

// C# program to check if a number is Harshad
// Number or not
using System;

public class GFG {

    // method to check Harshad Number
    static bool checkHarshad(int n)
    {

        // calculate sum of digits
        int sum = 0;
        for (int temp = n; temp > 0; temp /= 10)
            sum += temp % 10;

        // Return true if sum of digits is
        // multiple of n
        return (n % sum == 0);
    }

    // Driver program to test above functions
    public static void Main()
    {
        Console.WriteLine(checkHarshad(12) ? "Yes" : "No");

        Console.WriteLine(checkHarshad(15) ? "Yes" : "No");
    }
}

// This code is contributed by vt_m.

PHP

<?php
// php program to check if 
// a number is Harshad 
// Number or not.

// function to check 
// Harshad Number
function checkHarshad($n)
{
    // calculate sum of digits
    $sum = 0;
    for ($temp = $n; $temp > 0;
                     $temp /= 10)
        $sum += $temp % 10;

    // Return true if sum of
    // digits is multiple of n
    return ($n % $sum == 0);
}

// Driver Code
$k = checkHarshad(12) ? "Yes\n" : "No\n";
     echo($k);
$k = checkHarshad(15) ? "Yes\n" : "No\n";
     echo($k);

// This code is contributed by ajit.
?>

JavaScript

<script>
    // Javascript program to check if a number is Harshad Number or not
    
    // method to check Harshad Number
    function checkHarshad(n)
    {
 
        // calculate sum of digits
        let sum = 0;
        for (let temp = n; temp > 0; temp = parseInt(temp / 10, 10))
            sum += temp % 10;
 
        // Return true if sum of digits is
        // multiple of n
        return (n % sum == 0);
    }
    
    document.write(checkHarshad(12) ? "Yes" + "</br>" : "No" + "</br>");
 
      document.write(checkHarshad(15) ? "Yes" + "</br>" : "No" + "</br>");
        
</script>

Output :

Yes
No

Time complexity: O(log₁₀N) for given input N
Auxiliary space: O(1)

Method #2: Using string:

We have to convert the given number to a string by taking a new variable.
Traverse the string, Convert each element to an integer and add this to the sum.
If the number is divisible by the sum then it is Harshad number.

Below is the implementation of the above approach:

C++

// C++ implementation of above approach
#include<bits/stdc++.h>
using namespace std;

string checkHarshad(int n)
{
    
    // Converting integer to string
    string st = to_string(n);
    
    // Initialising sum to 0
    int sum = 0;
    int length = st.length();

    // Traversing through the string
    for(char i : st)
    {
        
        // Converting character to int
        sum = sum + (i - '0');
    }
    
    // Comparing number and sum
    if (n % sum == 0)
    {
        return "Yes";
    }
    else
    {
        return "No";
    }
}

// Driver Code
int main()
{
    int number = 18;
    
    // Passing this number to get result function
    cout << checkHarshad(number) << endl;
}

// This code is contributed by rrrtnx

Java

import java.io.*;
// java code to check the given number is Harshad or not
class GFG
{
  // function to check that given number
  // is Harshad or not.
    static String checkHarshad(int n)
    {
      
      // converting the integer to string
        String st = Integer.toString(n);
        int sum = 0;
      
      // calculating total number of digits
      // in a number
        int length=st.length();
      
      // adding the all digits of a number
        for(int i = 0; i < length; i++){
            sum += st.charAt(i)-'0';
        }
      
      // checking that sum is divisior of n or not
        if(n % sum == 0){
           return "YES";
        }
        else{
            return "NO";
        }
    }
  
  // driver code
    public static void main(String args[]){
        int number = 18;
      
      // function call
        System.out.println(checkHarshad(number));
    } 
}

// This code is contributed by Machhaliya Muhammad

Python3

# Python implementation of above approach
def checkHarshad(n):
  
    # Converting integer to string
    st = str(n)
    
    # Initialising sum to 0
    sum = 0
    length = len(st)

    # Traversing through the string
    for i in st:

        # Converting character to int
        sum = sum + int(i)
        
    # Comparing number and sum
    if (n % sum == 0):
        return "Yes"
    else:
        return "No"


# Driver Code
number = 18
# passing this number to get result function
print(checkHarshad(number))

# This code is contributed by vikkycirus

// C# program to find the radii
// of the three tangent circles
// of equal radius when the radius
// of the circumscribed circle is given
using System;

class GFG {
    static String checkHarshad(int n)
    {

        // Converting integer to string
        String st = n.ToString();

        // Initialising sum to 0
        int sum = 0;
        int length = st.Length;

        // Traversing through the string
        foreach(char i in st)
        {
            // Converting character to int
            sum = sum + (i - '0');
        }

        // Comparing number and sum
        if (n % sum == 0) {
            return "Yes";
        }
        else {
            return "No";
        }
    }

    // Driver code
    public static void Main()
    {
        int number = 18;

        // Passing this number to get result function
        Console.WriteLine(checkHarshad(number));
    }
}

// This code is contributed by Nidhi goel

JavaScript

<script>
// Javascript implementation of above approach
function checkHarshad(n){

    // Converting integer to string
    let st = String(n)
    
    // Initialising sum to 0
    let sum = 0
    let length = st.length

    // Traversing through the string
    for(i in st){
        // Converting character to int
        sum = sum + parseInt(i)
    }
        
    // Comparing number and sum
    if (n % sum == 0){
        return "Yes"
    }
    else{
        return "No"
    }
}

// Driver Code
let number = 18
// passing this number to get result function
document.write(checkHarshad(number))

// This code is contributed by _saurabh_jaiswal
</script>

Output

Yes

Time Complexity: O(n)
Auxiliary Space: O(n)

References:
https://en.wikipedia.org/wiki/Harshad_number

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