Smallest K digit number divisible by X (original) (raw)

Last Updated : 22 Jun, 2022

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.

Try It Yourself

C++ `

// C++ code to find smallest 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 MIN int MIN = pow(10, K - 1);

// MIN is the result
if (MIN % X == 0)
    return MIN;

// returning ans
return ((MIN + X) - ((MIN + X) % X));

}

// Driver Code int main() { // Number whose divisible is to be found int X = 83;

// Max K-digit divisible is to be found
int K = 5;

cout << answer(X, K);

}

Java

// Java code to find smallest 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 MIN double MIN = Math.pow(i, K - 1);

    // returning ans
    if (MIN % X == 0)
        return (MIN);
    else
        return ((MIN + X) - ((MIN + X) % X));
}

public static void main(String[] args)
{

    // Number whose divisible is to be found
    double X = 83;
    double K = 5;

    System.out.println((int)answer(X, K));
}

}

// Code contributed by Mohit Gupta_OMG <(0_o)>

Python3

Python code to find smallest K-digit

number divisible by X

def answer(X, K):

# Computing MAX
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));

Code contributed by Mohit Gupta_OMG <(0_o)>

C#

// C# code to find smallest K-digit // number divisible by X using System;

class GFG {

// Function to compute the result
public static double answer(double X, double K)
{

    double i = 10;

    // Computing MIN
    double MIN = Math.Pow(i, K - 1);

    // returning ans
    if (MIN % X == 0)
        return MIN;
    else
        return ((MIN + X) - ((MIN + X) % X));
}

// Driver code
public static void Main()
{

    // Number whose divisible is to be found
    double X = 83;
    double K = 5;

    Console.WriteLine((int)answer(X, K));
}

}

// This code is contributed by vt_m.

PHP

MIN=pow(10,MIN = pow(10, MIN=pow(10,K - 1); // MIN is the result if ($MIN % $X == 0) return $MIN; // returning ans return (($MIN + $X) - (($MIN + X)X) % X)X)); } // Driver Code // Number whose divisible // is to be found $X = 83; // Max K-digit divisible // is to be found $K = 5; echo answer($X, $K); // This code is contributed by ajit ?>

JavaScript

Output :

10043

Time Complexity: O(logk)

Auxiliary Space: O(1)