# 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++

 `// 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)); ` `    ``} ` `} `

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## 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
```