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

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

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++

 // CPP program to find minimum // sum of product of number #include 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; }

Java

 // 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));     } }

Python

 # 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

C#

 // 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.

PHP



Output:

7

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Improved By : nitin mittal, jit_t

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