Discrete Mathematics - "Prove that if p and q are primes and p∣q , then p=q"

Question

I'm not sure how i would go about proving this. Help would be much appreciated. This was a question on a revision task sheet for my Computing course. I understand that since p and p' are both prime, and as such can't be one, they must equal eachother since p divides p'. I am, however, stuck on the proof and what method i would use to prove this.

Answer 1

Suppose $p$ and $q$ are primes. And suppose that $p\vert q$. That means that $q=k*p$ for some integer $k$. But! Since $q$ is prime, it cannot be a product of two other integers. Except, if $k=1$. So $q=1*p$. $q=p$

Answer 2

Since $q$ divides $p$ , $q$ must be a prime factor of $p$. But Wait ! $p$ is itself a prime and it's only prime factors are $1,p$ , it should be one of those. Since $1$ is not a prime number , $\boxed{q=p}.$

Answer 3

$p\mid q$ says "$p$ divides $q$."

So, define the term "prime" in relation to "divides".