jmc

The factors of $36$ are $1,2,3,4,6,9,12,18,$ and $36$. The multiples of $4$ up to $36$ are $4,8,12,16,20,24,28,32$ and $36$. Only $4,12$ and $36$ appear on both lists, so the answer is $3$, which is option $\boxed{3}$.