I'm not looking for an answer as I would like to do it myself as much as possible, even if it's with help.
The problem:
The number 12 may be factored into three positive integers in exactly eighteen ways, these factorizations include 1 × 3 × 4, 2 × 2 × 3 and 2 × 3 × 2. Let N be the number of seconds in a week. In how many ways can N be factored into three positive integers?
If this is a really easy question I'm going to feel really stupid after this.
Thanks for any help! :)
Hint: This is all about the fundamental theorem of arithmetic, that being that every number can be broken down uniquely into a product of primes
So first write down $N$ as a product of primes by breaking down $$7\cdot 24\cdot 60\cdot 60$$ (7 days, 24 hours, 60 hours, 60 seconds), each into primes. Now, you are including permutations in your solutions which can complicate things, but what you are doing is you are splitting the primes into 3 piles (some of which can be empty). Figure out how many ways there are to do that