how many factors of 72 are even

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. 

The even factors of 72 are

2, 4, 6, 8, 12, 18, 24, 36, 72

how many factors of 72 are even

1. Prime Factorization: $$72 =2^3*3^2$$

2. how many factors of 72 are even: 

   $$\small{\text{ $ \begin{array}{lrll} 2.1 & 2^{ \textcolor[rgb]{1,0,0}{3} } &:& \qquad { \textcolor[rgb]{1,0,0}{3} } $ factors: $ 2^1 = 2 \quad 2^2 = 4 \quad 2^3 = 8\\\\ 2.2& 2^{ \textcolor[rgb]{1,0,0}{3} }*3^{ \textcolor[rgb]{1,0,0}{2} } & :& \qquad { \textcolor[rgb]{1,0,0}{3}* \textcolor[rgb]{1,0,0}{2} } =6 $ factors: $ 2^1*3^1 = 6 \quad 2^2*3^1 = 12 \quad 2^3*3^1 = 24\\ &&&\qquad $ and $ 2^1*3^2 = 18 \quad 2^2*3^2 = 36 \quad 2^3*3^2 = 72 \end{array} $ }}$$