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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 divisble 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
class IsDivisible
{
    // Function to find that number 
    // is divisble 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 divisble 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 divisble 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 divisble 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.
?>


Output:

Yes

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

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