Suppose that a is a group element and $a^6 = e$. What are the possibilities for $|a|$? 
Suppose that $a$ is a group element and $a^6 = e$. What are the possibilities for $|a|$? (Gallian, Contemporary Abstract Algebra, Exercise 18, Chapter 3.)

I just started looking at Abstract Algebra again and I was stuck on this question. It will probably be extremely simple for all of you but I didn't know what to do.
I tried doing regular operations like those found in arithmetic but obviously, that is one of the reasons why Abstract Algebra is so difficult.

Wouldn’t it just be the divisors of 6?  
For instance, if $|a| = 2$, then $a^6$ would be $e$, in virtue of:

$a^6 = (a^2.a^2).a^2 = (e.e).e = e.e = e$

