What are the possible values of the integers $x, y , z$?

Question

So the question is Let $x,y, z$ Be digits so that the $9$-digit number $5x36y98z2$ is divisible by $792$.

$1) ~$ Without calculating $x$ and $y$, explain why $z = 3$ or $ 7$.

$2)~$ Without calculating $x$, show that $y = 0$ or $9$.

$3)~$ Find all combinations of $x, y, z$