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Largest K digit number divisible by X
  • Difficulty Level : Basic
  • Last Updated : 16 Apr, 2021

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.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 

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