Find the Largest Good Number in Divisors of Given Number n in C++

In this problem, we are given a number N. Our task is to find the largest good number in the divisors of given number N.

A good number is a number in which every digit is larger than the sum of digits of its right (all less significant bits than it). For example, 732 is a good number, 7> 3+2 and 3>2.

Let's take an example to understand the problem,

Input : N = 15
Output : 15

Explanation −

Divisors of 15 : 1, 3, 5, 15.

Solution Approach

A simple solution to the problem is by finding all the divisors of N. And they find the largest good number which is extracted as a product of all prime divisors of the number.

Example

Program to illustrate the working of our solution

#include <bits/stdc++.h>
using namespace std;
int findLargestGoodNumber(int n){
   vector<int> primeFactors;
   int x = n;
   for (int i = 2; i * i <= n; i++) {
      if (x % i == 0) {
         primeFactors.push_back(i);
         while (x % i == 0) 
            x /= i;
      }
   }
   if (x > 1) 
      primeFactors.push_back(x);
   int goodNumber = 1;
   for (int i = 0; i < primeFactors.size(); i++)
      goodNumber = goodNumber * primeFactors[i];
   return goodNumber;
}
int main(){
   int n = 28;
   cout<<"The largest good Number in divisor of "<<n<<" is "<<findLargestGoodNumber(n); 
   return 0;
}

Example

The largest good Number in divisor of 28 is 14