# 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 10^{i}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` `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

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