# 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); ` `} ` |

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## 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)> ` |

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## 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)> ` |

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## 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. ` |

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## 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 ` `?> ` |

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**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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