Understandng euclids theorem Reading this Wikipedia article, it states "If q is not prime, then some prime factor p divides q"
Why does some prime factor divide q? Does mean that for any number there is some prime factor p that divides q?

Here's a method for proving thr statement. By definition, if q is not prime, then q has some divisors, other than 1 and q itself. Let d be a divisor of q.
We now have two cases:
1) if d is prime, then we've found a prime number that divides q, and we're done.
2) if d is not prime, then it has some divisors. Let d' a divisor of d, different of 1 and d itself. I assume you know that if d divides q, and d' divides d, then d' also divides q. So if our new d' is prime, then we're done. Otherwise, we apply the same reasoning for a divisor of d', different of 1 and d' itself, which of course, will divide q.
Eventually, we will obtain a prime dvisor.
I know this isn't a very rigorous proof, but it helps you get an ideea of why the statement is indeed correct.
