Question 67
$x$, $y$ and $z$ are distinct 2-digit positive integers. The first digit of $x$ is equal to the second digit of $y$, the first digit of $y$ is equal to the second digit of $z$, and the first digit of $z$ is equal to the second digit of $x$. How many positive integers can be the greatest common divisor of $x$, $y$ and $z$?