C++ Program for Largest K digit number divisible by X?

In this problem we will try to find largest K-digit number, that will be divisible by X. To do this task we will take the largest K digit number by this formula ((10^k) – 1). Then check whether the number is divisible by X or not, if not, we will get the exact number by using this formula.

???−(??? ??? ?)

One example is like a 5-digit number, that is divisible by 29. So the largest 5-digit number is 99999. This is not divisible by 29. Now by applying the formula we will get −

99999−(99999 ??? 29)=99999−7=99992

The number 99992 is divisible by 29.

Algorithm

maxKDigit(k, x)

begin
   max = (10^k) - 1
   if max is divisible by x, return max
   otherwise return max – (max mod x)
end

Example

 Live Demo

#include<iostream>
#include<cmath>
using namespace std;
long max_k_digit(int k, int x){
   //get the maximum number of k digits
   int max = pow(10, k) - 1;
   if(max % x == 0){
      return max;
   }
   return (max) - (max % x);
}
main() {
   int k, x;
   cout << "Enter Digit Count(K) and Divisor(N): ";
   cin >> k >> x;
   cout << "Result is: " << max_k_digit(k, x);
}

Output

Enter Digit Count(K) and Divisor(N): 5 29
Result is: 99992

Output

Enter Digit Count(K) and Divisor(N): 6 87
Result is: 999978