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++

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// 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;
}

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Java














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// 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"); 


    } 


}  



















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Python3














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# 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.  



















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C#














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// 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. 



















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PHP














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<?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. 


?> 



















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Output:


Yes



This article is contributed by  DANISH_RAZA . If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.


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