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



To minimize sum, we must factorize factors as long as possible. With this process, we prime factors. So to find minimum sum of product of number, we find sum of prime factors of product.

C++

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// 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;
}

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Java














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// Java program to find minimum 


// sum of product of number 


  


public class Main { 


  


    // To find minimum sum of 


    // product of number 


    static 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 


    public static void main(String[] args) 


    { 


        int num = 12; 


        System.out.println(findMinSum(num)); 


    } 


} 



















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Python














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# Python program to find minimum 


# sum of product of number 


   


# To find minimum sum of 


# product of number 


def findMinSum(num): 


    sum = 0


      


    # Find factors of number 


    # and add to the sum 


    i = 2


    while(i * i <= num): 


        while(num % i == 0): 


            sum += i 


            num /= i 


        i += 1


    sum += num 


      


    # Return sum of numbers 


    # having minimum product 


    return sum


  


# Driver Code 


num = 12


print findMinSum(num) 


  


# This code is contributed by Sachin Bisht 



















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C#














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// C# program to find minimum 


// sum of product of number 


using System;  


  


public class GFG { 


  


    // To find minimum sum of 


    // product of number 


    static 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 Code 


    public static void Main() 


    { 


        int num = 12; 


        Console.Write(findMinSum(num)); 


    } 


      


} 


  


// This Code is contributed by Nitin Mittal. 



















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PHP














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<?php 


// PHP program to find minimum 


// sum of product of number 


  


// To find minimum sum of 


// product of number 


function findMinSum($num) 


{ 


    $sum = 0; 


  


    // Find factors of number 


    // and add to the sum 


    for ($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 Code 


$num = 12; 


  


echo(findMinSum($num)); 


  


// This code is contributed by Ajit. 


?> 



















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Output:


7



This article is contributed by nuclode. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.


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Improved By :  nitin mittal, jit_t