# Check if a large number is divisible by 8 or not

Given a number, the task is to check if a number is divisible by 8 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 = 1128
Output : Yes

Input : n = 1124
Output : No

Input  : n = 363588395960667043875487
Output : No
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Since input number may be very large, we cannot use n % 8 to check if a number is divisible by 8 or not, especially in languages like C/C++. The idea is based on following fact.

A number is divisible by 8 if number formed by last three digits of it is divisible by 8.

Illustration:

```For example, let us consider 76952
Number formed by last three digits = 952
Since 952 is divisible by 8, 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 8 is 0 if i greater
than or equal to three. Note than 10000,
1000,... etc lead to remainder 0 when divided by 8.

So remainder of "7*10000 + 6*1000 + 9*100 +
5*10 + 2" divided by 8 is equivalent to remainder
of following :
0 + 0 + 9*100 + 5*10 + 2 = 52
Therefore we can say that the whole number is
divisible by 8 if 952 is divisible by 8.```

Below is implementation of above fact :

## C++

 `// C++ program to find if a number is divisible by ` `// 8 or not ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find that number divisible by ` `// 8 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'``)%8 == 0); ` ` `  `    ``// If there is double digit ` `    ``if` `(n == 2) ` `        ``return` `(((str[n-2]-``'0'``)*10 + (str[n-1]-``'0'``))%8 == 0); ` ` `  `    ``// If number formed by last three digits is ` `    ``// divisible by 8. ` `    ``int` `last = str[n-1] - ``'0'``; ` `    ``int` `second_last = str[n-2] - ``'0'``; ` `    ``int` `third_last = str[n-3] - ``'0'``; ` ` `  `    ``return` `((third_last*100 + second_last*10 + last) % 8 == 0); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``string str = ``"76952"``; ` `    ``check(str)?  cout << ``"Yes"` `: cout << ``"No "``; ` `    ``return` `0; ` `} `

## Java

 `// Java program to find if a number is ` `// divisible by 8 or not ` `class` `IsDivisible ` `{ ` `    ``// Function to find that number divisible by ` `    ``// 8 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'``)%``8` `== ``0``); ` `      `  `        ``// If there is double digit ` `        ``if` `(n == ``2``) ` `            ``return` `(((str.charAt(n-``2``)-``'0'``)*``10` `+ (str.charAt(n-``1``)-``'0'``))%``8` `== ``0``); ` `      `  `        ``// If number formed by last three digits is ` `        ``// divisible by 8. ` `        ``int` `last = str.charAt(n-``1``) - ``'0'``; ` `        ``int` `second_last = str.charAt(n-``2``) - ``'0'``; ` `        ``int` `third_last = str.charAt(n-``3``) - ``'0'``; ` `      `  `        ``return` `((third_last*``100` `+ second_last*``10` `+ last) % ``8` `== ``0``); ` `    ``} ` `     `  `    ``// main function ` `    ``public` `static` `void` `main (String[] args)  ` `    ``{ ` `        ``String str = ``"76952"``; ` `        ``if``(check(str)) ` `            ``System.out.println(``"Yes"``); ` `        ``else` `            ``System.out.println(``"No"``); ` `    ``} ` `}  `

## Python3

 `# Python 3 program to find  ` `# if a number is divisible ` `# by 8 or not ` ` `  ` `  `# Function to find that ` `# number divisible by 8 ` `# or not ` `def` `check(st) : ` `    ``n ``=` `len``(st) ` `     `  `    ``# Empty string ` `    ``if` `(n ``=``=` `0``) : ` `        ``return` `False` ` `  `    ``# If there is single digit ` `    ``if` `(n ``=``=` `1``) : ` `        ``return` `((``int``)(st[``0``]) ``%` `8` `=``=` `0``) ` ` `  `    ``# If there is double digit ` `    ``if` `(n ``=``=` `2``) : ` `        ``return` `((``int``)(st[n ``-` `2``]) ``*` `10` `+` `          ``((``int``)(``str``[n ``-` `1``]) ``%` `8` `=``=` `0``)) ` ` `  `    ``# If number formed by last ` `    ``# three digits is divisible ` `    ``# by 8. ` `    ``last ``=` `(``int``)(st[n ``-` `1``]) ` `    ``second_last ``=` `(``int``)(st[n ``-` `2``]) ` `    ``third_last ``=` `(``int``)(st[n ``-` `3``]) ` ` `  `    ``return` `((third_last``*``100` `+` `second_last``*``10` `+` `                               ``last) ``%` `8` `=``=` `0``) ` ` `  ` `  `# Driver code ` `st ``=` `"76952"` ` `  `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 8 or not ` `using` `System; ` ` `  `class` `IsDivisible ` `{ ` `    ``// Function to find that number  ` `    ``// divisible by 8 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'``) %8  == 0); ` `     `  `        ``// If there is double digit ` `        ``if` `(n == 2) ` `            ``return` `(((str[n - 2] - ``'0'``) * 10 +  ` `            ``(str[n - 1] - ``'0'``)) % 8 == 0); ` `     `  `        ``// If number formed by last three  ` `        ``// digits is divisible by 8 ` `        ``int` `last = str[n - 1] - ``'0'``; ` `        ``int` `second_last = str[n - 2] - ``'0'``; ` `        ``int` `third_last = str[n - 3] - ``'0'``; ` `     `  `        ``return` `((third_last * 100 + second_last   ` `                        ``* 10 + last) % 8 == 0); ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `Main ()  ` `    ``{ ` `        ``String str = ``"76952"``; ` `        ``if``(check(str)) ` `            ``Console.Write(``"Yes"``); ` `        ``else` `            ``Console.Write(``"No"``); ` `    ``} ` `}  ` ` `  `// This Code is contributed by Nitin Mittal. `

## PHP

 ` `

Output:

`Yes`

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Improved By : nitin mittal, jit_t

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