jmc

A positive integer is a factor of $n$ if and only if its prime factorization is of the form $2^a\cdot 3^b\cdot 5^c$ where $0\le a\le 3$, $0\le b\le 2$, and $0\le c\le 1$. An integer is even if and only if the exponent of 2 in its prime factorization is at least 1. Therefore, we have 3 choices for $a$, 3 choices for $b$ and $2$ choices for $c$, for a total of $(3)(3)(2)=\boxed{18}$ ways to form an even positive factor of $n$.