Smallest K digit number divisible by X
Integers X and K are given. The task is to find the smallest K-digit number divisible by X.
Examples :
Input : X = 83, K = 5
Output : 10043
10040 is the smallest 5 digit
number that is multiple of 83.
Input : X = 5, K = 2
Output : 10
A simple solution is to try all numbers starting from the smallest K digit number
(which is 100…(K-1)times) and return the first number divisible by X.
An efficient solution would be :
Compute MIN : smallest K-digit number (1000...(K-1)times)
If, MIN % X is 0, ans = MIN
else, ans = (MIN + X) - ((MIN + X) % X))
This is because there will be a number in
range [MIN...MIN+X] divisible by X.
C++
#include <bits/stdc++.h>
using namespace std;
int answer( int X, int K)
{
int MIN = pow (10, K - 1);
if (MIN % X == 0)
return MIN;
return ((MIN + X) - ((MIN + X) % X));
}
int main()
{
int X = 83;
int K = 5;
cout << answer(X, K);
}
|
Java
import java.io.*;
import java.lang.*;
class GFG {
public static double answer( double X, double K)
{
double i = 10 ;
double MIN = Math.pow(i, K - 1 );
if (MIN % X == 0 )
return (MIN);
else
return ((MIN + X) - ((MIN + X) % X));
}
public static void main(String[] args)
{
double X = 83 ;
double K = 5 ;
System.out.println(( int )answer(X, K));
}
}
|
Python3
def answer(X, K):
MIN = pow ( 10 , K - 1 )
if ( MIN % X = = 0 ):
return ( MIN )
else :
return (( MIN + X) - (( MIN + X) % X))
X = 83 ;
K = 5 ;
print (answer(X, K));
|
C#
using System;
class GFG {
public static double answer( double X, double K)
{
double i = 10;
double MIN = Math.Pow(i, K - 1);
if (MIN % X == 0)
return MIN;
else
return ((MIN + X) - ((MIN + X) % X));
}
public static void Main()
{
double X = 83;
double K = 5;
Console.WriteLine(( int )answer(X, K));
}
}
|
PHP
<?php
function answer( $X , $K )
{
$MIN = pow(10, $K - 1);
if ( $MIN % $X == 0)
return $MIN ;
return (( $MIN + $X ) -
(( $MIN + $X ) % $X ));
}
$X = 83;
$K = 5;
echo answer( $X , $K );
?>
|
Javascript
<script>
function answer(X, K)
{
let MIN = Math.pow(10, K - 1);
if (MIN % X == 0)
return MIN;
return ((MIN + X) -
((MIN + X) % X));
}
let X = 83;
let K = 5;
document.write(answer(X, K));
</script>
|
Output :
10043
Time Complexity: O(logk)
Auxiliary Space: O(1)
Last Updated :
22 Jun, 2022
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