Show that if n is even and $n≥ 2$ then $\phi(n)≤ n/2$

Question

I'm currently working in the following Euler's theorem exercise:

Show that if n is even and $n≥2$ then $\phi(n)≤ n/2$

I'm starting from the point that if $n$ is even at least one of its factors is $2$ but still can't find a way to show the required fact, any help will be really appreciated.

Answer 1

Since $n$ is even, any even number that's less than or equal $n$ is not coprime to $n$. There are $\frac n2$ of them. The inequality follows.