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. ` `?> ` |

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.

## Recommended Posts:

- Find sum of even factors of a number
- Find sum of odd factors of a number
- Sum of all the factors of a number
- Find largest prime factor of a number
- Maximum factors formed by two numbers
- Count ways to express a number as sum of consecutive numbers
- Minimum number with digits as 4 and 7 only and given sum
- Pell Number
- Finding power of prime number p in n!
- Find politeness of a number
- Prime Factorization using Sieve O(log n) for multiple queries
- Find all divisors of a natural number | Set 1
- Efficient program to print all prime factors of a given number
- Reservoir Sampling
- Program for Fibonacci numbers