# Check if a large number is divisible by 3 or not

Given a number, the task is that we divide number by 3. The input number may be large and it may not be possible to store even if we use long long int.

Examples:

Input : n = 769452 Output : Yes Input : n = 123456758933312 Output : No Input : n = 3635883959606670431112222 Output : Yes

Since input number may be very large, we cannot use n % 3 to check if a number is divisible by 3 or not, especially in languages like C/C++. The idea is based on following fact.

A number is divisible by 3 if sum of its digits is divisible by 3.

**Illustration:**

For example n = 1332 Sum of digits = 1 + 3 + 3 + 2 = 9 Since sum is divisible by 3, 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 3 is 1 So powers of 10 only result in value 1. Remainder of "1*1000 + 3*100 + 3*10 + 2" divided by 3 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 3, answer is yes.

Below is the implementation of above fact :

## C++

`// C++ program to find if a number is divisible by` `// 3 or not` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Function to find that number divisible by 3 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 3.` ` ` `return` `(digitSum % 3 == 0);` `}` `// Driver code` `int` `main()` `{` ` ` `string str = ` `"1332"` `;` ` ` `check(str)? cout << ` `"Yes"` `: cout << ` `"No "` `;` ` ` `return` `0;` `}` |

## Java

`// Java program to find if a number is` `// divisible by 3 or not` `class` `IsDivisible` `{` ` ` `// Function to find that number ` ` ` `// divisible by 3 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 3.` ` ` `return` `(digitSum % ` `3` `== ` `0` `);` ` ` `}` ` ` `// main function` ` ` `public` `static` `void` `main (String[] args) ` ` ` `{` ` ` `String str = ` `"1332"` `;` ` ` `if` `(check(str))` ` ` `System.out.println(` `"Yes"` `);` ` ` `else` ` ` `System.out.println(` `"No"` `);` ` ` `}` `} ` |

## Python3

`# Python program to find if a number is` `# divisible by 3 or not` `# Function to find that number ` `# divisible by 3 or not` `def` `check(num) :` ` ` ` ` `# Compute sum of digits` ` ` `digitSum ` `=` `0` ` ` `while` `num > ` `0` `:` ` ` `rem ` `=` `num ` `%` `10` ` ` `digitSum ` `=` `digitSum ` `+` `rem ` ` ` `num ` `=` `num ` `/` `10` ` ` ` ` `# Check if sum of digits is ` ` ` `# divisible by 3.` ` ` `return` `(digitSum ` `%` `3` `=` `=` `0` `)` ` ` `# main function` `num ` `=` `1332` `if` `(check(num)) :` ` ` `print` `(` `"Yes"` `)` `else` `:` ` ` `print` `(` `"No"` `)` ` ` `# This code is contributed by Nikita Tiwari.` |

## C#

`// C# program to find if a number is` `// divisible by 3 or not` `using` `System;` `class` `GFG` `{` ` ` `// Function to find that number ` ` ` `// divisible by 3 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 3.` ` ` `return` `(digitSum % 3 == 0);` ` ` `}` ` ` `// main function` ` ` `public` `static` `void` `Main () ` ` ` `{` ` ` `string` `str = ` `"1332"` `;` ` ` ` ` `if` `(check(str))` ` ` `Console.WriteLine(` `"Yes"` `);` ` ` `else` ` ` `Console.WriteLine(` `"No"` `);` ` ` `}` `} ` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to find if a ` `// number is divisible by` `// 3 or not` `// Function to find that` `// number divisible by 3 or not` `function` `check(` `$str` `)` `{` ` ` ` ` `// Compute sum of digits` ` ` `$n` `= ` `strlen` `(` `$str` `);` ` ` `$digitSum` `= 0;` ` ` `for` `(` `$i` `= 0; ` `$i` `< ` `$n` `; ` `$i` `++)` ` ` `$digitSum` `+= (` `$str` `[` `$i` `] - ` `'0'` `);` ` ` `// Check if sum of digits` ` ` `// is divisible by 3.` ` ` `return` `(` `$digitSum` `% 3 == 0);` `}` `// Driver code` `$str` `= ` `"1332"` `;` `$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` `// 3 or not` `// Function to find that` `// number divisible by 3 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 3.` ` ` `return` `(digitSum % 3 == 0);` `}` `// Driver code` `let str = ` `"1332"` `;` `let x = check(str) ? ` `"Yes"` `: ` `"No "` `;` `document.write(x);` `// This code is contributed by _saurabh_jaiswal.` `</script>` |

**Output**

Yes

**Time Complexity**: O(logn), where n is the given number.

**Auxiliary Space: **O(1), as we are not using any extra space.

**Method 2:** Checking given number is divisible by 3 or not by using the modulo division operator “%”.

## C++

`#include <iostream>` `using` `namespace` `std;` `int` `main()` `{` ` ` `//input` ` ` `long` `long` `int` `n=769452;` ` ` ` ` `// finding given number is divisible by 3 or not` ` ` `if` `(n % 3 ==0)` ` ` `{` ` ` `cout << ` `"Yes"` `;` ` ` `}` ` ` `else` ` ` `{` ` ` `cout << ` `"No"` `;` ` ` `}` ` ` ` ` `return` `0;` `}` `// This code is contributed by satwik4409.` |

## Java

`/*package whatever //do not write package name here */` `import` `java.io.*;` `class` `GFG {` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `// input` ` ` `long` `n = ` `769452` `;` ` ` `// 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 % ` `3` `== ` `0` `) {` ` ` `System.out.println(` `"Yes"` `);` ` ` `}` ` ` `else` `{` ` ` `System.out.println(` `"No"` `);` ` ` `}` ` ` `}` `}` `// This code is contributed by laxmigangarajula03` |

## Python3

`# Python code ` `# To check whether the given number is divisible by 3 or not` `#input ` `n` `=` `769452` `# the above input can also be given as n=input() -> taking input from user` `# finding given number is divisible by 3 or not` `if` `int` `(n)` `%` `3` `=` `=` `0` `:` ` ` `print` `(` `"Yes"` `) ` `else` `: ` ` ` `print` `(` `"No"` `)` ` ` `# this code is contributed by gangarajula laxmi` |

## C#

`using` `System;` `public` `class` `GFG{` ` ` `static` `public` `void` `Main (){` ` ` `//input` ` ` `long` `n = 769452;` ` ` `// 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 % 3 == 0)` ` ` `{` ` ` `Console.Write(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `Console.Write(` `"No"` `);` ` ` `} ` ` ` `}` `}` `// This code is contributed by laxmigangarajula03` |

## Javascript

`<script>` ` ` `// JavaScript code for the above approach` ` ` `// To check whether the given number is divisible by 3 or not` ` ` `//input ` ` ` `var` `n = 769452` ` ` ` ` `// finding given number is divisible by 3 or not` ` ` `if` `(n % 3 == 0)` ` ` `document.write(` `"Yes"` `)` ` ` `else` ` ` `document.write(` `"No"` `)` ` ` `// This code is contributed by Potta Lokesh` ` ` `</script>` |

**Output**

Yes

**Time Complexity:** O(1) as it is doing constant operations

**Auxiliary Space**: O(1)

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