  We consider typical finite dimensional complex irreducible representations of
a basic classical simple Lie superalgebra, and give a sufficient condition on
when unique factorization of finite tensor products of such representations
hold. We also prove unique factorization of tensor products of singly atypical
finite dimensional irreducible modules for $\mathfrak{sl}(m+1,n+1)$,
$\mathfrak{osp}(2,2n)$, $G(3)$ and $F(4)$ under an additional assumption. This
result is a Lie superalgebra analogue of Rajan's fundamental result
\cite{MR2123935} on unique factorization of tensor products for finite
dimensional complex simple Lie algebras.
