Related Articles

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

• Difficulty Level : Hard
• Last Updated : 21 Jun, 2021

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```

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%16
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``?>`

## Javascript

 ``

Output:

`35 is not divisible by 17`

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes arrow_drop_up