1) Prove that every composite number greater than 1 has at least one prime divisor.
To me, this sounds like the fundamental theorem of arithmetic (I could be dead wrong) and I have found various sites explaining that there are 2 parts to this proof...but I'm not sure if this is how I'm supposed to set it up.
2) Prove that every composite number n has at least one prime divisor which is =< sqrt(n).
3) Prove that every composite number can be represented as a product of primes.
The problem I'm having is that all these proofs seem very alike to me and I don't really know how to begin any of them. I know that every composite number can be broken down into a product of primes,but I don't really know how to show that explicitly.
Any help would be greatly appreciated!