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

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 <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;` `}` |

## 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

`<?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.` `?>` |

## Javascript

`<script>` `// Javascript program to find minimum` `// sum of product of number` ` ` `// To find minimum sum of` `// product of number` `function` `findMinSum(num)` `{` ` ` `let sum = 0;` ` ` ` ` `// Find factors of number` ` ` `// and add to the sum` ` ` `for` `(let 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` `let num = 12;` ` ` `document.write(findMinSum(num));` ` ` `// This code is contributed by _saurabh_jaiswal.` `</script>` |

**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.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the **Essential Maths for CP Course** at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**