# Check if a number is divisible by 17 using bitwise operators

Given a number n, check if it is divisible by 17 using bitwise operators.

Examples:

```Input : n = 34
Output : 34 is divisible by 17

Input :  n = 43
Output : 43 is not divisible by 17
```

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

A naive approach will be to check it by % operator if it leaves a remainder of 0.

To do division using Bitwise operators, we must rewrite the expression in powers of 2.

```n/17 = (16*n)/(17*16)
= (17 - 1)*n/(17*16)
= (n/16) - (n/(17*16))```

We can rewrite n/16 as floor(n/16) + (n%16)/16 using general rule of division.

```n/17 = floor(n/16) + (n%16)/16 -
(floor(n/16) + (n%16)/16)/17
= floor(n/16) - (floor(n/16) -
17*(n%16)/16 + (n%16)/16)/17
= floor(n/16) - (floor(n/16)-n%16)/17```

The left-hand-side of this equation is n/17. That will be an integer only when the right-hand-side is an integer. floor(n/16) is an integer by definition. So the whole left-hand-side would be an integer if (floor(n/16)-n%16)/17 is also an integer.

This implies n is divisible by 17 if (floor(n/16)-n%16) is divisible by 17.

(floor(n/16)-n%16) can be written in bitwise as (int)(n>>4) – (int)(n&15) where n>>4 means n/16 and n%15 means n%15

Below is the implementation of the above approach:

## CPP

 `// CPP program to check if a number is ` `// divisible by 17 or not using bitwise ` `// operator. ` `#include ` `using` `namespace` `std; ` ` `  `// function to check recursively if the ` `// number is divisible by 17 or not ` `bool` `isDivisibleby17(``int` `n) ` `{ ` `    ``// if n=0 or n=17 then yes ` `    ``if` `(n == 0 || n == 17) ` `        ``return` `true``; ` ` `  `    ``// if n is less then 17, not ` `    ``// divisible by 17 ` `    ``if` `(n < 17) ` `        ``return` `false``; ` ` `  `    ``// reducing the number by floor(n/16) ` `    ``// - n%16 ` `    ``return` `isDivisibleby17((``int``)(n >> 4) - (``int``)(n & 15)); ` `} ` ` `  `// driver code to check the above function ` `int` `main() ` `{ ` `    ``int` `n = 35; ` `    ``if` `(isDivisibleby17(n)) ` `        ``cout << n << ``" is divisible by 17"``; ` `    ``else` `        ``cout << n << ``" is not divisible by 17"``; ` `    ``return` `0; ` `} `

## Java

 `// Java program to check if a number is ` `// divisible by 17 or not using bitwise ` `// operator. ` `class` `GFG{ ` `     `  `    ``// function to check recursively if the ` `    ``// number is divisible by 17 or not ` `    ``static` `boolean` `isDivisibleby17(``int` `n) ` `    ``{ ` `         `  `        ``// if n=0 or n=17 then yes ` `        ``if` `(n == ``0` `|| n == ``17``) ` `            ``return` `true``; ` `     `  `        ``// if n is less then 17, not ` `        ``// divisible by 17 ` `        ``if` `(n < ``17``) ` `            ``return` `false``; ` `     `  `        ``// reducing the number by  ` `        ``// floor(n/16) - n%16 ` `        ``return` `isDivisibleby17((``int``)(n >> ``4``) ` `                            ``- (``int``)(n & ``15``)); ` `    ``} ` `     `  `    ``// driver function ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `n = ``35``; ` `        ``if` `(isDivisibleby17(n) == ``true``) ` `            ``System.out.printf ` `            ``(``"%d is divisible by 17"``,n); ` `        ``else` `            ``System.out.printf ` `            ``(``"%d is not divisible by 17"``,n); ` `    ``} ` `} ` ` `  `// This code is contributed by ` `// Smitha Dinesh Semwal `

## Python3

 `# Python 3 program to ` `# check if a number is ` `# divisible by 17 or ` `# not using bitwise ` `# operator. ` ` `  `# function to check recursively if the ` `# number is divisible by 17 or not ` `def` `isDivisibleby17(n): ` ` `  `    ``# if n=0 or n=17 then yes ` `    ``if` `(n ``=``=` `0` `or` `n ``=``=` `17``): ` `        ``return` `True` ` `  `    ``# if n is less then 17, not ` `    ``# divisible by 17 ` `    ``if` `(n < ``17``): ` `        ``return` `False` ` `  `    ``# reducing the number by floor(n/16) ` `    ``# - n%16 ` `    ``return` `isDivisibleby17((``int``)(n >> ``4``) ``-` `(``int``)(n & ``15``)) ` ` `  ` `  `# driver code to check the above function ` `n ``=` `35` `if` `(isDivisibleby17(n)): ` `    ``print``(n,``"is divisible by 17"``) ` `else``: ` `    ``print``(n,``"is not divisible by 17"``) ` ` `  `# This code is contributed by ` `# Smitha Dinesh Semwal `

## C#

 `// C# program to check if a number is ` `// divisible by 17 or not using bitwise ` `// operator. ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `    ``// function to check recursively if the ` `    ``// number is divisible by 17 or not ` `    ``static` `bool` `isDivisibleby17(``int` `n) ` `    ``{ ` `         `  `        ``// if n=0 or n=17 then yes ` `        ``if` `(n == 0 || n == 17) ` `            ``return` `true``; ` `     `  `        ``// if n is less then 17, not ` `        ``// divisible by 17 ` `        ``if` `(n < 17) ` `            ``return` `false``; ` `     `  `        ``// reducing the number by  ` `        ``// floor(n/16) - n%16 ` `        ``return` `isDivisibleby17((``int``)(n >> 4) ` `                            ``- (``int``)(n & 15)); ` `    ``} ` `     `  `    ``// Driver function ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `n = 35; ` `        ``if` `(isDivisibleby17(n) == ``true``) ` `            ``Console.WriteLine ` `            ``(n +``"is divisible by 17"``); ` `        ``else` `            ``Console.WriteLine ` `            ``( n+ ``" is not divisible by 17"``); ` `    ``} ` `} ` ` `  `// This code is contributed by ` `// vt_m `

## PHP

 `> 4) -  ` `                            ``(int)(``\$n` `& 15)); ` `} ` ` `  `    ``// Driver Code ` `    ``\$n` `= 35; ` `    ``if` `(isDivisibleby17(``\$n``)) ` `        ``echo` `\$n``.``" is divisible by 17"``; ` `    ``else` `        ``echo` `\$n``.``" is not divisible by 17"``; ` ` `  `// This code is contributed by mits  ` `?> `

Output:

```35 is not divisible by 17
```

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