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C++ Program for Smallest K digit number divisible by X?
In this problem we will try to find smallest K-digit number, that will be divisible by X. To do this task we will take the smallest 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.
(min+ 𝑋)−((min+ 𝑋) 𝑚𝑜𝑑 𝑋)
One example is like a 5-digit number, that is divisible by 29. So the smallest 5-digit number is 10000. This is not divisible by 29. Now by applying the formula we will get −
(10000+ 29)−((10000+29) 𝑚𝑜𝑑 29)=10029−24=10005
The number 10005 is divisible by 29.
Algorithm
minKDigit(k, x)
begin min = 10 ^ (k-1) if min is divisible by x, return min otherwise return (min + x) – ((min + x) mod x) end
Example
#include<iostream>
#include<cmath>
using namespace std;
long min_k_digit(int k, int x) {
//get the minimum number of k digits
int min = pow(10, k-1);
if(min % x == 0) {
return min;
}
return (min + x) - ((min + x) % x);
}
main() {
int k, x;
cout << "Enter Digit Count(K) and Divisor(N): ";
cin >> k >> x;
cout << "Result is: " << min_k_digit(k, x);
}Output
Enter Digit Count(K) and Divisor(N): 5 29 Result is: 10005
Output
Enter Digit Count(K) and Divisor(N): 6 87 Result is: 100050
Updated on: 30-Jul-2019
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