Find Nearest Integer with GCD Greater Than 1 in C++

Suppose we have a number N. Consider a function gcdSum(x) of a positive integer x which is the gcd of that integer with its sum of digits. We have to find the smallest integer x >= n, such that gcdSum(x) > 1.

So, if the input is like N = 31, then the output will be 33, because gcd of 31 and (3+1) is 1. The gcd of 32 and (3+2) is 1, and gcd of 33 and (3+3) is 3.

Steps

To solve this, we will follow these steps −

for initialize i := n, when i <= n + 2, update (increase i by 1), do:
   jml := 0
   x := i
   while x > 0, do:
      jml := jml + x mod 10
      x := x / 10
   if gcd of i and jml is not equal to 1, then:
      return i
return 0

Example

Let us see the following implementation to get better understanding −

#include <bits/stdc++.h>
using namespace std;

int solve(int n) {
   for (long i = n; i <= n + 2; i++) {
      long jml = 0;
      long x = i;
      while (x > 0) {
         jml += x % 10;
         x /= 10;
      }
      if (__gcd(i, jml) != 1) {
         return i;
      }
   }
   return 0;
}
int main() {
   int N = 31;
   cout << solve(N) << endl;
}

Input

31

Output

33