# Python Program for Find minimum sum of factors of number

• Difficulty Level : Hard
• Last Updated : 22 Jun, 2022

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```

## Python3

 `# 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`

Output:

`7`

Time Complexity: O(n1/2 * log n)

Auxiliary Space: O(1)

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

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