Degree of splitting field over F and irreducible polynomial

Question

Suppose $f(x) ∈ F[x]$ is irreducible of degree $n > 0$, and L is the splitting field of f(x) over F. I want to show that $n|[L : F]$ and also give an example to show that $n = [L : F]$ can occur.I know if $n$ is the degree of the minimal polynomial of a over $F$, then $[F(a) :F]=n$..but does that help?