Two elements a,b are associates if a|b and b|a.
So far, my thought process is the following: for $a, b \in \mathbb{Z}$, if b > a then a may divide b but clearly b cannot divide a since it's larger. So wouldn't there be one equivalence class for each integer, consisting of just that integer?
For two integers $a$ and $b$ , we have $ a|b$ and $ b|a$ if and only if $a=\pm b$
Thus each equivalence class is a set {$\pm a$}.
{$0$} ,{$\pm 1$}, {$\pm 2$}, {$\pm 3$}, {$\pm 4$},.....