# Largest K digit number divisible by X

Integers X and K are given. The task is to find the highest K-digit number divisible by X.**Examples:**

Input : X = 30, K = 3 Output : 990 990 is the largest three digit number divisible by 30. Input : X = 7, K = 2 Output : 98

A **simple solution** is to try all numbers starting from the largest K digit number (which is 999…K-times) and return the first number divisible by X.

An **efficient solution **is to use below formula.

ans = MAX - (MAX % X) where MAX is the largest K digit number which is 999...K-times

The formula works on simple school method division. We remove remainder to get the largest divisible number.

## C++

`// CPP code to find highest K-digit number divisible by X` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to compute the result` `int` `answer(` `int` `X, ` `int` `K)` `{` ` ` `// Computing MAX` ` ` `int` `MAX = ` `pow` `(10, K) - 1;` ` ` `// returning ans` ` ` `return` `(MAX - (MAX % X));` `}` `// Driver` `int` `main()` `{` ` ` `// Number whose divisible is to be found` ` ` `int` `X = 30;` ` ` `// Max K-digit divisible is to be found` ` ` `int` `K = 3;` ` ` `cout << answer(X, K);` `}` |

## Java

`// Java code to find highest` `// K-digit number divisible by X` `import` `java.io.*;` `import` `java.lang.*;` `class` `GFG {` ` ` `public` `static` `double` `answer(` `double` `X, ` `double` `K)` ` ` `{` ` ` `double` `i = ` `10` `;` ` ` `// Computing MAX` ` ` `double` `MAX = Math.pow(i, K) - ` `1` `;` ` ` `// returning ans` ` ` `return` `(MAX - (MAX % X));` ` ` `}` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `// Number whose divisible is to be found` ` ` `double` `X = ` `30` `;` ` ` `// Max K-digit divisible is to be found` ` ` `double` `K = ` `3` `;` ` ` `System.out.println((` `int` `)answer(X, K));` ` ` `}` `}` `// Code contributed by Mohit Gupta_OMG <(0_o)>` |

## Python3

`# Python code to find highest` `# K-digit number divisible by X` `def` `answer(X, K):` ` ` ` ` `# Computing MAX` ` ` `MAX` `=` `pow` `(` `10` `, K) ` `-` `1` ` ` ` ` `# returning ans` ` ` `return` `(` `MAX` `-` `(` `MAX` `%` `X))` `X ` `=` `30` `;` `K ` `=` `3` `;` `print` `(answer(X, K));` `# Code contributed by Mohit Gupta_OMG <(0_o)>` |

## C#

`// C# code to find highest` `// K-digit number divisible by X` `using` `System;` `class` `GFG {` ` ` ` ` `public` `static` `double` `answer(` `double` `X, ` `double` `K)` ` ` `{` ` ` ` ` `double` `i = 10;` ` ` ` ` `// Computing MAX` ` ` `double` `MAX = Math.Pow(i, K) - 1;` ` ` `// returning ans` ` ` `return` `(MAX - (MAX % X));` ` ` `}` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `// Number whose divisible is to be found` ` ` `double` `X = 30;` ` ` `// Max K-digit divisible is to be found` ` ` `double` `K = 3;` ` ` `Console.WriteLine((` `int` `)answer(X, K));` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP code to find highest K-digit` `// number divisible by X` `// Function to compute the result` `function` `answer(` `$X` `, ` `$K` `)` `{` ` ` ` ` `// Computing MAX` ` ` `$MAX` `= pow(10, ` `$K` `) - 1;` ` ` `// returning ans` ` ` `return` `(` `$MAX` `- (` `$MAX` `% ` `$X` `));` `}` `// Driver` ` ` `// Number whose divisible` ` ` `// is to be found` ` ` `$X` `= 30;` ` ` `// Max K-digit divisible` ` ` `// is to be found` ` ` `$K` `= 3;` ` ` `echo` `answer(` `$X` `, ` `$K` `);` `// This code is contributed by ajit` `?>` |

## Javascript

`<script>` `// Javascript code to find highest K-digit` `// number divisible by X` `// Function to compute the result` `function` `answer(X, K)` `{` ` ` ` ` `// Computing MAX` ` ` `let MAX = Math.pow(10, K) - 1;` ` ` `// returning ans` ` ` `return` `(MAX - (MAX % X));` `}` `// Driver` ` ` `// Number whose divisible` ` ` `// is to be found` ` ` `let X = 30;` ` ` `// Max K-digit divisible` ` ` `// is to be found` ` ` `let K = 3;` ` ` `document.write(answer(X, K));` `// This code is contributed by gfgking` `</script>` |

**Output:**

990

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

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