Determine $\gcd (a, a^2)$ where a is a non-zero integer.
Given that $a^2 = a \times a$, than $a$ is a factor of $a^2$.
Furthermore, $a$ is the largest factor of $a$. Therefore the largest factor of both is $a$.
However, $a$ could be negative, so we take. the modulus.
$$\gcd (a,a^2) = \lvert a \rvert$$