  Let $\mathcal A$ be a separable, unital, approximately divisible
C$^*$-algebra. We show that $\mathcal A$ is generated by two self-adjoint
elements and the topological free entropy dimension of any finite generating
set of $\mathcal A$ is less than or equal to 1. In addition, we show that the
similarity degree of $\mathcal A$ is at most 5. Thus an approximately divisible
C$^*$-algebra has an affirmative answer to Kadison's similarity problem.
