Suppose that $3$ is a factor of $a$, $a$ is a divisor of $12$, and $a$ is positive. What is the number of possible values of $a$?
To find the possible values of $a$, I need to list all the divisors of $12$ and see which ones are multiples of $3$. The divisors of $12$ are $1, 2, 3, 4, 6, 12$. Out of these, only $3, 6, 12$ are multiples of $3$. Therefore, there are $3$ possible values of $a$. 