If $p$ is a factor of $m^2$ then $p$ is a factor of $m$ I'm a complete beginner and not sure where to go with this proof of Euclid's lemma. Any help would be greatly appreciated.

If $m$ is a positive integer and a prime number $p$ is a factor of $m^2,$ then  $p$ is a factor of $m.$

So far I have:
Since we know that $m$ is a positive integer, then $m^2$ must also be positive.
We also know that $p$ is positive integer, since it is a prime number.
So $m^2 = p*k$ where $k$ is positive since both $m^2$ and $p$ are positive.
Therefore, $k$ is greater than or equal to $1.$
...?

Put $\,k = m\,$ in Euclid's Lemma: $ $ prime $\:p\:|\:m\,k\:\Rightarrow\: p\:|\:m\ \ or\ \ p\:|\:k,\,$  proved here & here & here.
