  In this paper, we obtain results for factorizability of quantum channels.
Firstly, we prove that if a tensor $T\otimes S_k$ of a quantum channel $T$ on
$M_n(\mathbb{C})$ with the completely depolarizing channel $S_k$ is written as
a convex combination of automorphisms on the matrix algebra
$M_n(\mathbb{C})\otimes M_k(\mathbb{C})$ with rational coefficients, then the
quantum channel $T$ has an exact factorization through some matrix algebra with
the normalized trace. Next, we prove that if a quantum channel has an exact
factorization through a finite dimensional von Neumann algebra with a convex
combination of normal faithful tracial states with rational coefficients, then
it also has an exact factorization through some matrix algebra with the
normalized trace.
