Check if the sum of digits of number is divisible by all of its digits

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Given an integer N, the task is to check whether the sum of digits of the given number is divisible by all of its digits or not. If divisible then print Yes else print No.

Examples:

Input: N = 12
Output: No
Sum of digits = 1 + 2 = 3
3 is divisible by 1 but not 2.

Input: N = 123
Output: Yes

Approach: First find the sum of the digits of the number then one by one check, whether the calculated sum is divisible by all the digits of the number. If for some digit it is not divisible then print No else print Yes.

Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function that returns true if all the digits
// of n divide the sum of the digits of n
bool isDivisible(long long int n)
{
 
    // Store a copy of the original number
    long long int temp = n;
 
    // Find the sum of the digits of n
    int sum = 0;
    while (n) {
        int digit = n % 10;
        sum += digit;
        n /= 10;
    }
 
    // Restore the original value
    n = temp;
 
    // Check if all the digits divide
    // the calculated sum
    while (n) {
        int digit = n % 10;
 
        // If current digit doesn't
        // divide the sum
        if (sum % digit != 0)
            return false;
 
        n /= 10;
    }
 
    return true;
}
 
// Driver code
int main()
{
    long long int n = 123;
 
    if (isDivisible(n))
        cout << "Yes";
    else
        cout << "No";
 
    return 0;
}

Java

// Java implementation of the approach 
public class GFG 
{
     
    // Function that returns true if all the digits 
    // of n divide the sum of the digits of n 
    static boolean isDivisible(long n) 
    { 
     
        // Store a copy of the original number 
        long temp = n; 
     
        // Find the sum of the digits of n 
        int sum = 0; 
        while (n != 0) 
        { 
            int digit = (int) n % 10; 
            sum += digit; 
            n /= 10; 
        } 
     
        // Restore the original value 
        n = temp; 
     
        // Check if all the digits divide 
        // the calculated sum 
        while (n != 0) 
        { 
            int digit = (int)n % 10; 
     
            // If current digit doesn't 
            // divide the sum 
            if (sum % digit != 0) 
                return false; 
     
            n /= 10; 
        } 
        return true; 
    } 
     
    // Driver code 
    public static void main (String[] args) 
    { 
        long n = 123; 
     
        if (isDivisible(n)) 
            System.out.println("Yes"); 
        else
            System.out.println("No"); 
    }
}
 
// This code is contributed by AnkitRai01

Python

# Python implementation of the approach
 
# Function that returns true if all the digits
# of n divide the sum of the digits of n
def isDivisible(n):
 
    # Store a copy of the original number
    temp = n
 
    # Find the sum of the digits of n
    sum = 0
    while (n):
        digit = n % 10
        sum += digit
        n //= 10
 
    # Restore the original value
    n = temp
 
    # Check if all the digits divide
    # the calculated sum
    while(n): 
        digit = n % 10
 
        # If current digit doesn't
        # divide the sum
        if(sum % digit != 0): 
            return False
 
        n //= 10;
 
    return True
 
# Driver code
n = 123
if(isDivisible(n)):
    print("Yes")
else:
    print("No")

C#

// C# implementation of the approach
using System;
 
class GFG
{
     
    // Function that returns true if all the digits 
    // of n divide the sum of the digits of n 
    static bool isDivisible(long n) 
    { 
     
        // Store a copy of the original number 
        long temp = n; 
     
        // Find the sum of the digits of n 
        int sum = 0; 
        while (n != 0) 
        { 
            int digit = (int) n % 10; 
            sum += digit; 
            n /= 10; 
        } 
     
        // Restore the original value 
        n = temp; 
     
        // Check if all the digits divide 
        // the calculated sum 
        while (n != 0) 
        { 
            int digit = (int)n % 10; 
     
            // If current digit doesn't 
            // divide the sum 
            if (sum % digit != 0) 
                return false; 
     
            n /= 10; 
        } 
        return true; 
    } 
     
    // Driver code 
    static public void Main ()
    {
        long n = 123; 
     
        if (isDivisible(n)) 
            Console.Write("Yes"); 
        else
            Console.Write("No"); 
    }
}
 
// This code is contributed by @tushil.

Javascript

<script>
 
// Javascript implementation of the approach     
 
// Function that returns true if all the
// digits of n divide the sum of the digits 
// of n
function isDivisible(n)
{
     
    // Store a copy of the original number
    var temp = n;
 
    // Find the sum of the digits of n
    var sum = 0;
     
    while (n != 0)
    {
        var digit = parseInt(n % 10);
        sum += digit;
        n = parseInt(n / 10);
    }
 
    // Restore the original value
    n = temp;
 
    // Check if all the digits divide
    // the calculated sum
    while (n != 0)
    {
        var digit = parseInt(n % 10);
 
        // If current digit doesn't
        // divide the sum
        if (sum % digit != 0)
            return false;
 
        n = parseInt(n/10);
    }
    return true;
}
 
// Driver code
var n = 123;
 
if (isDivisible(n))
    document.write("Yes");
else
    document.write("No");
 
// This code is contributed by todaysgaurav
 
</script>

Output

Yes

Time Complexity: O(log(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 integer and add this to sum.
Traverse the string again
Check if the sum is not divisible by any one of the digits
If it is true then return False
Else return True

Below is the implementation of above approach:

C++

// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;
 
string getResult(int n)
{
 
    // Converting integer to string
    string st = to_string(n);
 
    // Initialising sum to 0
    int sum = 0;
    int length = st.size();
 
    // Traversing through the string
    for (int i = 0; i < st.size(); i++) {
 
        // Converting character to int
        sum = sum + (int(st[i]) - 48);
    }
 
    // Comparing number and sum
    // Traversing again
    for (int i = 0; i < st.size(); i++) {
 
        // Check if any digit is
        // not dividing the sum
        if (sum % (int(st[i]) - 48) != 0) {
 
            // Return false
            return "No";
        }
 
        // If any value is not returned
        // then all the digits are dividing the sum
        // SO return true
        else {
            return "Yes";
        }
    }
}
 
// Driver Code
int main()
{
    int n = 123;
 
    // passing this number to get result function
    cout << getResult(n);
    return 0;
}
 
// This code is contributed by subhamkumarm348.

Java

// Java implementation of the approach
import java.io.*;
import java.util.*; 
 
class GFG
{
     // Function that returns true if all the digits
     // of n divide the sum of the digits of n
     public static String getResult(int n)
     {
         // Converting integer to string
         String st = String.valueOf(n);  
          
         // Initialising sum to 0
         int sum = 0;
         int length = st.length();
          
         // Traversing through the string
         for (int i = 0; i < length; i++) 
         {
             // Converting character to int
             int c = st.charAt(i)-48;
             sum += c;
         }
          
         // Comparing number and sum
         // Traversing again
         for (int i = 0; i < length; i++) 
         {
             // Check if any digit is
             // not dividing the sum
             int c = st.charAt(i)-48;
             if (sum % c != 0) 
             {
                 // Return false
                 return "No";
             }
              
             // If any value is not returned
             // then all the digits are dividing the sum
             // SO return true
             else
             {
                 return "Yes";
             }
         }
         return "No";
    }
      
    // Driver code
    public static void main (String[] args)
    {
        int n = 123;
         
        // passing this number to get result function
        System.out.println(getResult(n));
    }
}
  
// This code is contributed by aditya942003patil

Python3

# Python implementation of above approach
def getResult(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
    # Traversing again
    for i in st:
       
        # Check if any digit is 
        # not dividing the sum
        if(sum % int(i) != 0):
             
            # Return false
            return 'No'
           
    # If any value is not returned 
    # then all the digits are dividing the sum
    # SO return true
    return 'Yes'
 
 
# Driver Code
n = 123
 
# passing this number to get result function
print(getResult(n))
 
# this code is contributed by vikkycirus

C#

// C# program to implement above approach
using System;
using System.Collections.Generic;
  
class GFG
{
   
  static string getResult(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
    for (int i = 0; i < length; i++) {
  
        // Converting character to int
        sum = sum + ((int)st[i] - 48);
    }
  
    // Comparing number and sum
    // Traversing again
    for (int i = 0; i < length; i++) {
  
        // Check if any digit is
        // not dividing the sum
        if (sum % ((int)st[i] - 48) != 0) {
            return "No";
        }
  
        // If any value is not returned
        // then all the digits are dividing the sum
        // SO return true
        else {
            return "Yes";
        }
    }
     
    return "No";
  }
  
  // Driver Code
  public static void Main(string[] args){
  
    int n = 123;
  
    // Function call
    Console.Write(getResult(n));
  }
}
  
// This code is contributed by adityapatil12.

Javascript

<script>
 
// JavaScript implementation of above approach
 
function getResult(n){
    
    // Converting integer to string
    var st = n.toString();
      
    // Initialising sum to 0
    var sum = 0
    var length = st.length;
  
    // Traversing through the string
    for (var i= 0 ;i<st.length ; i++){
  
        // Converting character to int
        sum = sum + Number(st[i])
    }
          
    // Comparing number and sum
    // Traversing again
    for( var i = 0 ; i < st.length ; i++){
        
        // Check if any digit is
        // not dividing the sum
        if(sum % Number(st[i]) != 0){
              
            // Return false
            return 'No'
        }
            
    // If any value is not returned
    // then all the digits are dividing the sum
    // SO return true
        else{
            return 'Yes';
          }
    }
      
 
}
  
  
// Driver Code
var n = 123;
  
// passing this number to get result function
document.write(getResult(n));
 
 
</script>

Output

Yes

Time Complexity: O(n), where n represents the length of the given string.
Auxiliary Space: O(d), where d represents the number of digits in the string.

Approach 3: Dynamic Programming:

The dynamic programming approach to check if a number is divisible by the sum of its digits works as follows:

Convert the given number to a string.
Calculate the sum of the digits of the number.
Initialize a boolean array dp of size sum+1, where dp[i] indicates whether it is possible to obtain a sum of i using some of the digits of the number.
Initialize dp[0] to true, since it is always possible to obtain a sum of 0 using no digits.
Traverse the digits of the number one by one. For each digit, traverse the dp array from right to left and update the values of dp[i] as follows:
a. If i is less than the current digit, then dp[i] remains unchanged.
b. If i is greater than or equal to the current digit, then dp[i] is updated as dp[i] || dp[i – digit], where digit is the current digit.
Return dp[sum], which indicates whether it is possible to obtain a sum of sum using some of the digits of the number.
If dp[sum] is true, then the sum of the digits of the number is divisible by the number itself, otherwise it is not divisible.

Here is the code for above approach:

C++

// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;
 
// Dynamic programming approach to check if a number is divisible
// by the sum of its digits
bool isDivisible(int n)
{
    // Convert the number to string
    string str = to_string(n);
 
    // Calculate the sum of digits
    int sum = 0;
    for (char c : str) {
        sum += (c - '0');
    }
 
    // If the sum is 0, return false
    if (sum == 0) {
        return false;
    }
 
    // Initialize the dp array
    bool dp[sum + 1];
    memset(dp, false, sizeof(dp));
    dp[0] = true;
 
    // Traverse the digits of the number
    for (char c : str) {
        int digit = c - '0';
        for (int i = sum; i >= digit; i--) {
            dp[i] = dp[i] || dp[i - digit];
        }
    }
 
    // Return true if the sum is divisible by the number
    return dp[sum];
}
int main()
{
    long long int n = 123;
  
    if (isDivisible(n))
        cout << "Yes";
    else
        cout << "No";
  
    return 0;
}

Java

import java.util.Arrays;
 
public class Main {
  // Dynamic programming approach to check if a number is divisible
// by the sum of its digits
static boolean isDivisible(int n) {
    // Convert the number to string
    String str = Integer.toString(n);
 
    // Calculate the sum of digits
    int sum = 0;
    for (char c : str.toCharArray()) {
        sum += (c - '0');
    }
 
    // If the sum is 0, return false
    if (sum == 0) {
        return false;
    }
 
    // Initialize the dp array
    boolean[] dp = new boolean[sum + 1];
    Arrays.fill(dp, false);
    dp[0] = true;
 
    // Traverse the digits of the number
    for (char c : str.toCharArray()) {
        int digit = c - '0';
        for (int i = sum; i >= digit; i--) {
            dp[i] = dp[i] || dp[i - digit];
        }
    }
 
    // Return true if the sum is divisible by the number
    return dp[sum];
}
 
public static void main(String[] args) {
    int n = 123;
 
    if (isDivisible(n)) {
        System.out.println("Yes");
    } else {
        System.out.println("No");
    }
}
}

Python3

class Program:
    @staticmethod
    def IsDivisible(n):
        # Convert the number to string
        str_n = str(n)
 
        # Calculate the sum of digits
        digit_sum = sum(int(digit) for digit in str_n)
 
        # If the sum is 0, return False
        if digit_sum == 0:
            return False
 
        # Initialize the dp array
        dp = [False] * (digit_sum + 1)
        dp[0] = True
 
        # Traverse the digits of the number
        for digit_char in str_n:
            digit = int(digit_char)
            for i in range(digit_sum, digit - 1, -1):
                dp[i] = dp[i] or dp[i - digit]
 
        # Return True if the sum is divisible by the number
        return dp[digit_sum]
 
    @staticmethod
    def Main():
        n = 123
 
        if Program.IsDivisible(n):
            print("Yes")
        else:
            print("No")
 
        # This code is contributed by Shivam Tiwari
 
 
# Run the program
Program.Main()

C#

using System;
 
public class Program
{
    // Dynamic programming approach to check if a number is divisible
    // by the sum of its digits
    public static bool IsDivisible(long n)
    {
        // Convert the number to string
        string str = n.ToString();
 
        // Calculate the sum of digits
        int sum = 0;
        foreach (char c in str)
        {
            sum += (c - '0');
        }
 
        // If the sum is 0, return false
        if (sum == 0)
        {
            return false;
        }
 
        // Initialize the dp array
        bool[] dp = new bool[sum + 1];
        dp[0] = true;
 
        // Traverse the digits of the number
        foreach (char c in str)
        {
            int digit = c - '0';
            for (int i = sum; i >= digit; i--)
            {
                dp[i] = dp[i] || dp[i - digit];
            }
        }
 
        // Return true if the sum is divisible by the number
        return dp[sum];
    }
 
    public static void Main()
    {
        long n = 123;
 
        if (IsDivisible(n))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
 
        // This code is contributed by Shivam Tiwari
    }
}

Javascript

// Dynamic programming approach to check if a number is divisible
// by the sum of its digits
function isDivisible(n) {
    // Convert the number to string
    let str = n.toString();
 
    // Calculate the sum of digits
    let sum = 0;
    for (let i = 0; i < str.length; i++) {
        sum += parseInt(str[i]);
    }
 
    // If the sum is 0, return false
    if (sum === 0) {
        return false;
    }
 
    // Initialize the dp array
    let dp = new Array(sum + 1).fill(false);
    dp[0] = true;
 
    // Traverse the digits of the number
    for (let i = 0; i < str.length; i++) {
        let digit = parseInt(str[i]);
        for (let j = sum; j >= digit; j--) {
            dp[j] = dp[j] || dp[j - digit];
        }
    }
 
    // Return true if the sum is divisible by the number
    return dp[sum];
}
 
let n = 123;
 
if (isDivisible(n)) {
    console.log("Yes");
} else {
    console.log("No");
}

Output

Yes

Time Complexity: O(SN), where S is the sum of the digits of the number and N is the number of digits in the number.
Auxiliary Space: O(S), as we are using a boolean array of size S+1 to store the intermediate results of the subproblems.

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