# Java 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

 `// 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)); ` `    ``} ` `} `

Output:

```7
```

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

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