How do I find the prime factorization of numbers with variables and exponents in them

Okay so the problem is this:
Find the greatest common factor of 180a^2 and 210a.
What I do is I find the prime factorization and select the greatest common factor from there.
However, I don't know how to do this with variables and exponents (I wasn't in class for this).
Thank you, any help is appreciated! :)

GCF of 180 and 210 is 30.
a^2 and a is a.
Therefore GCF of 180a^2 and 210a is 30a.

180a^2 and 210a
a(180a and 210
=30a(6a and 7)

Ans

30 a