# Check if a large number is divisible by 4 or not

Given a number, the task is to check if a number is divisible by 4 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 = 1124 Output : Yes Input : n = 1234567589333862 Output : No Input : n = 363588395960667043875487 Output : No

Since input number may be very large, we cannot use n % 4 to check if a number is divisible by 4 or not, especially in languages like C/C++. The idea is based on following fact.

A number is divisible by 4 if number formed by last two digits of it is divisible by 4.

**Illustration:**

For example, let us consider 76952Number formed by last two digits = 52 Since 52 is divisible by 4, answer is YES.

**How does this work?**

Let us consider 76952, we can write it as 76942 = 7*10000 + 6*1000 + 9*100 + 5*10 + 2 The proof is based on below observation: Remainder of 10^{i}divided by 4 is 0 if i greater than or equal totwo. Note than 100, 1000, ... etc lead to remainder 0 when divided by 4. So remainder of "7*10000 + 6*1000 + 9*100 + 5*10 + 2" divided by 4 is equivalent to remainder of following : 0 + 0 + 0 + 5*10 + 2 = 52 Therefore we can say that the whole number is divisible by 4 if 52 is divisible by 4.

Below is implementation of above idea :

## C++

`// C++ program to find if a number is divisible by` `// 4 or not` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find that number divisible by` `// 4 or not` `bool` `check(string str)` `{` ` ` `int` `n = str.length();` ` ` `// Empty string` ` ` `if` `(n == 0)` ` ` `return` `false` `;` ` ` `// If there is single digit` ` ` `if` `(n == 1)` ` ` `return` `((str[0] - ` `'0'` `) % 4 == 0);` ` ` `// If number formed by last two digits is` ` ` `// divisible by 4.` ` ` `int` `last = str[n - 1] - ` `'0'` `;` ` ` `int` `second_last = str[n - 2] - ` `'0'` `;` ` ` `return` `((second_last * 10 + last) % 4 == 0);` `}` `// Driver code` `int` `main()` `{` ` ` `string str = ` `"76952"` `;` ` ` ` ` `// Function call` ` ` `check(str) ? cout << ` `"Yes"` `: cout << ` `"No "` `;` ` ` `return` `0;` `}` |

## Java

`// Java program to find if a number is` `// divisible by 4 or not` `class` `IsDivisible` `{` ` ` `// Function to find that number` ` ` `// is divisible by 4 or not` ` ` `static` `boolean` `check(String str)` ` ` `{` ` ` `int` `n = str.length();` ` ` `// Empty string` ` ` `if` `(n == ` `0` `)` ` ` `return` `false` `;` ` ` `// If there is single digit` ` ` `if` `(n == ` `1` `)` ` ` `return` `((str.charAt(` `0` `) - ` `'0'` `) % ` `4` `== ` `0` `);` ` ` `// If number formed by last two digits is` ` ` `// divisible by 4.` ` ` `int` `last = str.charAt(n - ` `1` `) - ` `'0'` `;` ` ` `int` `second_last = str.charAt(n - ` `2` `) - ` `'0'` `;` ` ` `return` `((second_last * ` `10` `+ last) % ` `4` `== ` `0` `);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `String str = ` `"76952"` `;` ` ` ` ` `// Function call` ` ` `if` `(check(str))` ` ` `System.out.println(` `"Yes"` `);` ` ` `else` ` ` `System.out.println(` `"No"` `);` ` ` `}` `}` |

## Python3

`# Python 3 program to find` `# if a number is divisible` `# by 4 or not` `# Function to find that` `# number divisible by` `# 4 or not` `def` `check(st):` ` ` `n ` `=` `len` `(st)` ` ` `# Empty string` ` ` `if` `(n ` `=` `=` `0` `):` ` ` `return` `False` ` ` `# If there is single` ` ` `# digit` ` ` `if` `(n ` `=` `=` `1` `):` ` ` `return` `((st[` `0` `] ` `-` `'0'` `) ` `%` `4` `=` `=` `0` `)` ` ` `# If number formed by` ` ` `# last two digits is` ` ` `# divisible by 4.` ` ` `last ` `=` `(` `int` `)(st[n ` `-` `1` `])` ` ` `second_last ` `=` `(` `int` `)(st[n ` `-` `2` `])` ` ` `return` `((second_last ` `*` `10` `+` `last) ` `%` `4` `=` `=` `0` `)` `# Driver code` `st ` `=` `"76952"` `# Function call` `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 4 or not` `using` `System;` `class` `GFG` `{` ` ` `// Function to find that number` ` ` `// is divisible by 4 or not` ` ` `static` `bool` `check(String str)` ` ` `{` ` ` `int` `n = str.Length;` ` ` `// Empty string` ` ` `if` `(n == 0)` ` ` `return` `false` `;` ` ` `// If there is single digit` ` ` `if` `(n == 1)` ` ` `return` `((str[0] - ` `'0'` `) % 4 == 0);` ` ` `// If number formed by last two` ` ` `// digits is divisible by 4.` ` ` `int` `last = str[n - 1] - ` `'0'` `;` ` ` `int` `second_last = str[n - 2] - ` `'0'` `;` ` ` `return` `((second_last * 10 + last) % 4 == 0);` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `String str = ` `"76952"` `;` ` ` `// Function call` ` ` `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` `// 4 or not` `// Function to find that` `// number divisible by` `// 4 or not` `function` `check(` `$str` `)` `{` ` ` `$n` `= ` `strlen` `(` `$str` `);` ` ` `// Empty string` ` ` `if` `(` `$n` `== 0)` ` ` `return` `false;` ` ` `// If there is single digit` ` ` `if` `(` `$n` `== 1)` ` ` `return` `((` `$str` `[0] - ` `'0'` `) % 4 == 0);` ` ` `// If number formed by` ` ` `// last two digits is` ` ` `// divisible by 4.` ` ` `$last` `= ` `$str` `[` `$n` `- 1] - ` `'0'` `;` ` ` `$second_last` `= ` `$str` `[` `$n` `- 2] - ` `'0'` `;` ` ` `return` `((` `$second_last` `* 10 + ` `$last` `) % 4 == 0);` `}` `// Driver code` `$str` `= ` `"76952"` `;` `// Function call` `$x` `= check(` `$str` `)? ` `"Yes"` `: ` `"No"` `;` `echo` `(` `$x` `);` `// This code is contributed by Ajit.` `?>` |

## Javascript

`//Javascript program to check whether a string is divisible by 4 or not` `// function to check the divisibility` `function` `check(str)` `{ ` ` ` `// checking the length for future reference` ` ` `var` `n = str.length;` ` ` `// if it is empty then directly returning false` ` ` `if` `( n == 0)` ` ` `{ ` ` ` `return` `false` `;` ` ` `}` ` ` ` ` `if` `( n == 1)` ` ` `{` ` ` `return` `((str[0] -` `'0'` `) % 4 == 0);` ` ` `}` ` ` `var` `lastNumber = str[n-1] -` `'0'` `;` ` ` `var` `lastSecondNUmber = str[n-2] -` `'0'` `;` ` ` `return` `((lastSecondNUmber * 10 + lastNumber) % 4 == 0); ` `}` `// Driver code` `var` `str=` `"76952"` `;` `//checking the value by passing it into the function` `// Function call` `if` `(check(str)){` ` ` `console.log(` `"Yes"` `);` `}` `else` `{` ` ` `console.log(` `"No"` `);` `}` |

**Output**

Yes

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