Check if a large number is divisible by 9 or not

Given a number, the task is to find if the number is divisible by 9 or not. The input number may be large and it may not be possible to store even if we use long long int.

Examples: 

Input  : n = 69354
Output : Yes

Input  : n = 234567876799333
Output : No

Input  : n = 3635883959606670431112222
Output : No

Since input number may be very large, we cannot use n % 9 to check if a number is divisible by 9 or not, especially in languages like C/C++. The idea is based on following fact. 

A number is divisible by 9 if sum of its digits is divisible by 9.

Illustration:

For example n = 9432
Sum of digits = 9 + 4 + 3 + 2
             = 18
Since sum is divisible by 9,
answer is Yes.

How does this work?

Let us consider 1332, we can write it as
1332 = 1*1000 + 3*100 + 3*10 + 2

The proof is based on below observation:
Remainder of 10i divided by 9 is 1
So powers of 10 only results in remainder 1 
when divided by 9.

Remainder of "1*1000 + 3*100 + 3*10 + 2"
divided by 9 can be written as : 
1*1 + 3*1 + 3*1 + 2 = 9
The above expression is basically sum of
all digits.

Since 9 is divisible by 9, answer is yes.

Below is the implementation of above idea.

C++

// C++ program to find if a number is divisible by
// 9 or not
#include<bits/stdc++.h>
using namespace std;

// Function to find that number divisible by 9 or not
int check(string str)
{
    // Compute sum of digits
    int n = str.length();
    int digitSum = 0;
    for (int i=0; i<n; i++)
        digitSum += (str[i]-'0');

    // Check if sum of digits is divisible by 9.
    return (digitSum % 9 == 0);
}

// Driver code
int main()
{
    string str = "99333";
    check(str)?  cout << "Yes" : cout << "No ";
    return 0;
}

Java

// Java program to find if a number is
// divisible by 9 or not
import java.io.*;
class IsDivisible
{
    // Function to find that number
    // is divisible by 9 or not
    static boolean check(String str)
    {
        // Compute sum of digits
        int n = str.length();
        int digitSum = 0;
        for (int i=0; i<n; i++)
            digitSum += (str.charAt(i)-'0');

        // Check if sum of digits is divisible by 9.
        return (digitSum % 9 == 0);
    }

    // main function
    public static void main (String[] args)
    {
        String str = "99333";
        if(check(str))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}

Python3

# Python 3 program to
# find if a number is
# divisible by
# 9 or not

# Function to find that
# number divisible by 9
# or not
def check(st) :

    # Compute sum of digits
    n = len(st)
    digitSum = 0

    for i in range(0,n) :
        digitSum = digitSum + (int)(st[i])

    # Check if sum of digits
    # is divisible by 9.
    return (digitSum % 9 == 0)

# Driver code
st = "99333"

if(check(st)) :
    print("Yes")
else :
    print("No")

# This code is contributed by Nikita Tiwari.

C#

// C# program to find if a number is
// divisible by 9 or not.
using System;

class GFG {

    // Function to find that number
    // is divisible by 9 or not
    static bool check(String str)
    {

        // Compute sum of digits
        int n = str.Length;
        int digitSum = 0;
        for (int i = 0; i < n; i++)
            digitSum += (str[i] - '0');

        // Check if sum of digits is
        // divisible by 9.
        return (digitSum % 9 == 0);
    }

    // main function
    public static void Main ()
    {
        String str = "99333";
        if(check(str))
            Console.Write("Yes");
        else
            Console.Write("No");
    }
}

// This code is Contributed by
// nitin mittal.

PHP

<?php
// PHP program to find if a number
// is divisible by 9 or not

// Function to find that
// number divisible by 9 or not
function check($str)
{

    // Compute sum of digits
    $n = strlen($str);
    $digitSum = 0;
    for ($i = 0; $i < $n; $i++)
        $digitSum += ($str[$i] - '0');

    // Check if sum of digits
    // is divisible by 9.
    return ($digitSum % 9 == 0);
}

// Driver code
$str = "99333";
$x = check($str) ? "Yes" : "No ";
echo($x);

// This code is contributed by Ajit.
?>

Javascript

<script>

// Javascript program to find if a number
// is divisible by 9 or not

// Function to find that
// number divisible by 9 or not
function check(str)
{

    // Compute sum of digits
    let n = str.length;
    let digitSum = 0;

    for(let i = 0; i < n; i++)
        digitSum += (str[i] - '0');

    // Check if sum of digits
    // is divisible by 9.
    return (digitSum % 9 == 0);
}

// Driver code
let str = "99333";
let x = check(str) ? "Yes" : "No ";

document.write(x);

// This code is contributed by _saurabh_jaiswal.

</script>

Output

Yes

Time Complexity: O(logN), as we are traversing the digits which will effectively costs logN time.
Auxiliary Space: O(1), as we are not using any extra space. 

Method 2: Checking given number is divisible by 9 or not by using the modulo division operator “%”.  

C++

#include <iostream>
using namespace std;

int main() {

  // input
    long long int n = 3635883959606670431112222;

    // the above input can also be given as n=input() ->
    // taking input from user finding given number is
    // divisible by 7 or not
    if (n % 9 == 0) {
      cout<<"Yes";
    }
    else {
      cout<<"No";
    }

    return 0;
}

// This code is contributed by laxmigangarajula03

Java

/*package whatever //do not write package name here */
// java program to check if given number is divisible by 9 or
// not using modulo division

import java.io.*;
import java.math.BigInteger;

class GFG {
  public static void main (String[] args)
  {

    // input number
    BigInteger n, b1,b2;

    n = new BigInteger("3635883959606670431112222");
    b1 = new BigInteger("9");

    // apply mod() method
    BigInteger result = n.mod(b1);
    // checking if the given number is divisible by 9 or not
    // using modulo division operator if the output of num%7
    // is equal to 0 then given number is divisible by 9
    // otherwise not divisible by 9
    b2 = new BigInteger("0");
    int comparevalue = result.compareTo(b2);
    if (comparevalue==0) {
      System.out.println("Yes");
    }
    else {
      System.out.println("No");
    }

  }
}

// This code is contributed by satwik4409.

Python3

# Python code
# To check whether the given number is divisible by 9 or not

#input
n=3635883959606670431112222
# the above input can also be given as n=input() -> taking input from user
# finding given number is divisible by 9 or not
if int(n)%9==0:
  print("Yes")
else:
  print("No")

  # this code is contributed by gangarajula laxmi

C#

using System;

public class GFG {

  static public void Main()
  {

    // input
    double n = 36358839596066;

    // the above input can also be given as n=input() ->
    // taking input from user finding given number is
    // divisible by 7 or not
    if (n % 9 == 0) {
      Console.Write("Yes");
    }
    else {
      Console.Write("No");
    }
  }
}

// This code is contributed by laxmigangarajula03

Javascript

<script>
        // JavaScript code for the above approach
        //input
var n=3635883959606670431112222

// finding given number is divisible by 9 or not
if (n%9==0)
  document.write("Yes")
else
  document.write("No")

    // This code is contributed by Potta Lokesh
    </script>

PHP

<?php
// PHP program to check
// if a large number is
// divisible by 11.

  // Driver Code
  // input number
$num = 3635883959606670431112222;

// finding given number is divisible by 11 or not
if ( $num % 9 == 0)
    echo " divisible";
else
    echo "not divisible";


?>

Output

No

Time complexity: O(1) it is performing constant operations
Auxiliary space: O(1)

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