Fastest way to find the order of x in a Finite Field

Question

Working on $\mathbb{F}_2[x]$, I want to find the less $n$ than $f(x)=x^8+x^6+x^5+x+1$ is a divisor of $x^n -1$. This is the same than finding the order of $[x]$ in the quotient $\frac{\mathbb{F}_2[x]}{<f(x)>}$, isomorphic to $\mathbb{F}_{256}$. One way is trying $[x^n]$ for every $n | 255$. Are there any other ways to find the order?