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# Check the divisibility of Hexadecimal numbers

• Last Updated : 13 May, 2021

Given a string S consisting of a large hexadecimal number, the task is to check its divisibility by a given decimal number M. If divisible then print Yes else print No.
Examples:

Input: S = “10”, M = 4
Output: Yes
10 is 16 in decimal and (16 % 4) = 0
Input: S = “10”, M = 5
Output: No

Approach: An approach used in this article will be used to avoid overflow. Iterate the entire string from the back-side.
If the remainder of the sub-string S[0…i] is known on division with M. Let’s call this remainder as R. This can be used to get the remainder when the substring S[0…i+1] is divided. To do that, first left shift the string S[0…i] by 1. This will be equivalent to multiplying the string by 16. Then, add S[i+1] to this and take its mod with M. With a little bit of modular arithmetic it boils down to

S[0…i+1] % M = (S[0…i] * 16 + S[i+1]) % M = ((S[0…i] % M * 16) + S[i+1]) % M

Thus, continue the above steps till the end of the string. If the final remainder is 0 then the string is divisible otherwise it is not.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `const` `string CHARS = ``"0123456789ABCDEF"``;``const` `int` `DIGITS = 16;` `// Function that returns true``// if s is divisible by m``bool` `isDivisible(string s, ``int` `m)``{``    ``// Map to map characters to real values``    ``unordered_map<``char``, ``int``> mp;` `    ``for` `(``int` `i = 0; i < DIGITS; i++) {``        ``mp[CHARS[i]] = i;``    ``}` `    ``// To store the remainder at any stage``    ``int` `r = 0;` `    ``// Find the remainder``    ``for` `(``int` `i = 0; i < s.size(); i++) {``        ``r = (r * 16 + mp[s[i]]) % m;``    ``}` `    ``// Check the value of remainder``    ``if` `(!r)``        ``return` `true``;``    ``return` `false``;``}` `// Driver code``int` `main()``{``    ``string s = ``"10"``;``    ``int` `m = 3;` `    ``if` `(isDivisible(s, m))``        ``cout << ``"Yes"``;``    ``else``        ``cout << ``"No"``;` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.util.*;` `class` `GFG``{` `static` `char` `[]CHARS = ``"0123456789ABCDEF"``.toCharArray();``static` `int` `DIGITS = ``16``;` `// Function that returns true``// if s is divisible by m``static` `boolean` `isDivisible(String s, ``int` `m)``{``    ``// Map to map characters to real values``    ``Map mp = ``new` `HashMap<>();` `    ``for` `(``int` `i = ``0``; i < DIGITS; i++)``    ``{        ``        ``mp. put(CHARS[i], i);``    ``}` `    ``// To store the remainder at any stage``    ``int` `r = ``0``;` `    ``// Find the remainder``    ``for` `(``int` `i = ``0``; i < s.length(); i++)``    ``{``        ``r = (r * ``16` `+ mp.get(s.charAt(i))) % m;``    ``}` `    ``// Check the value of remainder``    ``if` `(r == ``0``)``        ``return` `true``;``    ``return` `false``;``}` `// Driver code``public` `static` `void` `main(String []args)``{``    ``String s = ``"10"``;``    ``int` `m = ``3``;` `    ``if` `(isDivisible(s, m))``        ``System.out.println(``"Yes"``);``    ``else``        ``System.out.println(``"No"``);``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 implementation of the approach``CHARS ``=` `"0123456789ABCDEF"``;``DIGITS ``=` `16``;` `# Function that returns true``# if s is divisible by m``def` `isDivisible(s, m) :` `    ``# Map to map characters to real value``    ``mp ``=` `dict``.fromkeys(CHARS, ``0``);` `    ``for` `i ``in` `range``( DIGITS) :``        ``mp[CHARS[i]] ``=` `i;` `    ``# To store the remainder at any stage``    ``r ``=` `0``;` `    ``# Find the remainder``    ``for` `i ``in` `range``(``len``(s)) :``        ``r ``=` `(r ``*` `16` `+` `mp[s[i]]) ``%` `m;` `    ``# Check the value of remainder``    ``if` `(``not` `r) :``        ``return` `True``;``        ` `    ``return` `False``;` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:``    ` `    ``s ``=` `"10"``;``    ``m ``=` `3``;` `    ``if` `(isDivisible(s, m)) :``        ``print``(``"Yes"``);``    ``else` `:``        ``print``(``"No"``);` `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach``using` `System;``using` `System.Collections.Generic;` `class` `GFG``{` `static` `char` `[]CHARS = ``"0123456789ABCDEF"``.ToCharArray();``static` `int` `DIGITS = 16;` `// Function that returns true``// if s is divisible by m``static` `bool` `isDivisible(String s, ``int` `m)``{``    ``// Map to map characters to real values``    ``Dictionary<``char``, ``int``> mp = ``new` `Dictionary<``char``, ``int``>();` `    ``for` `(``int` `i = 0; i < DIGITS; i++)``    ``{        ``        ``if``(mp.ContainsKey(CHARS[i]))``            ``mp[CHARS[i]] = i;``        ``else``            ``mp.Add(CHARS[i], i);``    ``}` `    ``// To store the remainder at any stage``    ``int` `r = 0;` `    ``// Find the remainder``    ``for` `(``int` `i = 0; i < s.Length; i++)``    ``{``        ``r = (r * 16 + mp[s[i]]) % m;``    ``}` `    ``// Check the value of remainder``    ``if` `(r == 0)``        ``return` `true``;``    ``return` `false``;``}` `// Driver code``public` `static` `void` `Main(String []args)``{``    ``String s = ``"10"``;``    ``int` `m = 3;` `    ``if` `(isDivisible(s, m))``        ``Console.WriteLine(``"Yes"``);``    ``else``        ``Console.WriteLine(``"No"``);``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``
Output:
`No`

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