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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 asa convex combination of automorphisms on the matrix algebra$M_n(\mathbb{C})\otimes M_k(\mathbb{C})$ with rational coefficients, then thequantum channel $T$ has an exact factorization through some matrix algebra withthe normalized trace. Next, we prove that if a quantum channel has an exactfactorization through a finite dimensional von Neumann algebra with a convexcombination of normal faithful tracial states with rational coefficients, thenit also has an exact factorization through some matrix algebra with thenormalized trace.

On tensors of factorizable quantum channels with the completely depolarizing channel