# Java Program to Find minimum sum of factors of number

Given a number, find minimum sum of its factors.

Examples:

Input : 12 Output : 7Explanation: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

`// 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

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