Why don't you count them
2,4,6,8,12,18,24,36,72
You had bes check, I might have made a mistake or missed one.
how many factors of 72 are even
1. Prime Factorization: $$72 =2^3*3^2$$
2. how many factors of 72 are even:
$$\small{\text{
$
\begin{array}{lrll}
2.1 &
2^{ \textcolor[rgb]{1,0,0}{3} } &:&
\qquad { \textcolor[rgb]{1,0,0}{3} } $ factors: $ 2^1 = 2 \quad 2^2 = 4 \quad 2^3 = 8\\\\
2.2&
2^{ \textcolor[rgb]{1,0,0}{3} }*3^{ \textcolor[rgb]{1,0,0}{2} } & :&
\qquad { \textcolor[rgb]{1,0,0}{3}* \textcolor[rgb]{1,0,0}{2} } =6 $ factors: $ 2^1*3^1 = 6 \quad 2^2*3^1 = 12 \quad 2^3*3^1 = 24\\
&&&\qquad $ and $ 2^1*3^2 = 18 \quad 2^2*3^2 = 36 \quad 2^3*3^2 = 72
\end{array}
$
}}$$