Here is a problem in my hand that I need so solve it. It sounds like this: Given a number (between 4 and 30000) x, which is the greatest number that can be written as a product made from numbers that have the sum x.

Example:

For x = 7 the result is 12.

Explanation:

12 = 2 x 3 x 3

7 = 2 + 2 + 3

I do not want to abridge the path for solving the problem and I do not want complete code for this problem. I only need some directions and documentation about the method that I could use in order to solve it.