Deriving classical Hall effect from quantum Hall effect

I’m interested in the derivation of the classical Hall effect coefficient, given in cgs by $$R_{H}=-frac{1}{nec},$$ where $n$ is the electron number density, $-e<0$ is the electron charge,and $c$ is the usual, ubiquitous velocity in Physics, from the fact that QHE provides the quantum of electrical conductance $$g=frac{2e^{2}}{h},$$ where $h$ is Planck’s constant, and the 2 comes from spin degeneracy.

Is there a convenient way to go from the quantum to the classical case for this problem?