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Check if a large number is divisible by 9 or not

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  • Difficulty Level : Basic
  • Last Updated : 06 Feb, 2023
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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;
 
    // finding given number is
    // divisible by 9 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%9
    // 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;
 
     // 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)

This article is contributed by DANISH_RAZA . If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 


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