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++

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// 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














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// 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














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# 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#














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// 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














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<?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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