# 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 76952
Number 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 10i divided by 4 is 0 if i greater
than or equal to two. 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 ` `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'``) % 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'``) % 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

 ``

## 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'``) % 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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