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

• Difficulty Level : Basic
• Last Updated : 30 Mar, 2023

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```

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 the implementation of the 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``import` `java.io.*;``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

 ``

## Javascript

 ``

Output

`Yes`

Time Complexity: O(1), as we are not using any loops for traversing.
Auxiliary Space: O(1), as we are not using any extra space.

Another Approach(Using Bitwise Operator):

The binary representation of the number 8 is 1000. If a number is divisible by 8, it means that its last three bits in binary representation are 000. Therefore, we can check if a number is divisible by 8 by checking if its last three bits are 000 or not.

To do this, we perform a bitwise AND operation between the input number and 7 (which is 111 in binary and has its last three bits set to 0). If the result of the bitwise AND operation is 0, then the input number is divisible by 8, otherwise it is not divisible by 8.

Note that we use long long int data type to handle large numbers.

## C++

 `#include ` `bool` `isDivisibleBy8(``long` `long` `int` `n) {``    ``return` `(n & 7) == 0; ``// 7 is 0111 in binary``}` `int` `main() {``    ``long` `long` `int` `n = 76952;` `    ``if` `(isDivisibleBy8(n)) {``        ``std::cout << n << ``" is divisible by 8\n"``;``    ``} ``else` `{``        ``std::cout << n << ``" is not divisible by 8\n"``;``    ``}` `    ``return` `0;``}`

## Java

 `import` `java.util.*;` `public` `class` `Main {``    ``// Function to check if a number is divisible by 8``    ``static` `boolean` `isDivisibleBy8(``long` `n) {``        ``return` `(n & ``7``) == ``0``; ``// 7 is 0111 in binary``    ``}` `    ``public` `static` `void` `main(String[] args) {``        ``long` `n = ``76952``;` `        ``if` `(isDivisibleBy8(n)) {``            ``System.out.println(n + ``" is divisible by 8"``);``        ``} ``else` `{``            ``System.out.println(n + ``" is not divisible by 8"``);``        ``}``    ``}``}`

## Python3

 `def` `isDivisibleBy8(n: ``int``) ``-``> ``bool``:``    ``return` `(n & ``7``) ``=``=` `0`  `# 7 is 0111 in binary` `n ``=` `76952``if` `isDivisibleBy8(n):``    ``print``(n, ``"is divisible by 8"``)``else``:``    ``print``(n, ``"is not divisible by 8"``)`

## C#

 `using` `System;` `public` `class` `Program {``  ``// Function to check if a number is divisible by 8``  ``static` `bool` `isDivisibleBy8(``long` `n) {``    ``return` `(n & 7) == 0; ``// 7 is 0111 in binary``  ``}` `  ``public` `static` `void` `Main(``string``[] args) {``    ``long` `n = 76952;` `    ``if` `(isDivisibleBy8(n)) {``      ``Console.WriteLine(n + ``" is divisible by 8"``);``    ``} ``else` `{``      ``Console.WriteLine(n + ``" is not divisible by 8"``);``    ``}``  ``}``}`

## Javascript

 `function` `isDivisibleBy8(n) {``    ``return` `(n & 7) == 0; ``// 7 is 0111 in binary``}` `let n = 76952;``if` `(isDivisibleBy8(n)) {``    ``console.log(n + ``" is divisible by 8"``);``} ``else` `{``    ``console.log(n + ``" is not divisible by 8"``);``}`

Output

`76952 is divisible by 8`

Time Complexity: O(1)
Auxiliary Space: O(1)

This article is contributed by DANISH_RAZA . If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.