C Program to Find minimum sum of factors of number

Given a number, find minimum sum of its factors.

Examples:

Input : 12
Output : 7
Explanation: 
Following are different ways to factorize 12 and
sum of factors in different ways.
12 = 12 * 1 = 12 + 1 = 13
12 = 2 * 6 = 2 + 6 = 8
12 = 3 * 4 = 3 + 4 = 7
12 = 2 * 2 * 3 = 2 + 2 + 3 = 7
Therefore minimum sum is 7

Input : 105
Output : 15

// CPP program to find minimum
// sum of product of number
#include <bits/stdc++.h>
using namespace std;

// To find minimum sum of
// product of number
int findMinSum(int num)
{
    int sum = 0;

    // Find factors of number
    // and add to the sum
    for (int i = 2; i * i <= num; i++) {
        while (num % i == 0) {
            sum += i;
            num /= i;
        }
    }
    sum += num;

    // Return sum of numbers
    // having minimum product
    return sum;
}

// Driver program to test above function
int main()
{
    int num = 12;

    cout << findMinSum(num);

    return 0;
}

Output:

7

Please refer complete article on Find minimum sum of factors of number for more details!

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