Possible Duplicate:
Euler $\Phi$ Function
$\underline{Question}$ Compute $\phi(24)$. For each element $\mathbb Z /24$ decide whether the element is a unit or a zero divisor. If the element is a unit, give its order and find its inverse.
$\underline {Answer}$ let $\,\,n=24=2\cdot3\cdot 3 \,\,,\, (\mathbb Z /24)$ ={$\bar1,\bar5,\bar7,\bar11,\bar13,\bar17,\bar19,\bar23$}
$\phi(24)=8$
How would i go about deciding whether each of the elements are a unit or zero divisor?