If $p$ is a prime and $p$ divides $a^3$ then $p$ divides $a$

Question

I have to either give a proof or provide a counterexample for this question. $a, b$ are non-zero intergers.

If $p$ is a prime and $p|a^3$ then $p|a$

I think this is true but do not know how to go about proving this question.

Answer 1

If $p$ divides $a^2\times a$ then $p$ divides $a^2$ or $a$ by Euclid's lemma. If it divides $a$ we are done, if it divides $a^2$ we can use euclid's lemma again.