# Check the divisibility of Hexadecimal numbers

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

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

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 `

Output:

```No
```

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Improved By : AnkitRai01, 29AjayKumar