An example of what I'm looking for will probably explain the question best. 24 can be written as:
- 12 · 2
- 6 · 2 · 2
- 3 · 2 · 2 · 2
- 8 · 3
- 4 · 2 · 3
- 6 · 4
I'm familiar with finding all the prime factors of a number ($24 = 3 · 2^3$), as well as all the factor pairs (24 = 12·2, 8·3, 6·4). I'm assuming one or both will form the basis of the answer, but I can't figure out an algorithm to find all the possible ways to represent a number as a product of 2 or more other numbers. So, what is a (preferably efficient) way to accomplish this?
Note: this is not homework, it's just for my own knowledge.