  In this paper we introduce the notion of factorization in the Hopf quasigroup
setting and we prove that, if $A$ and $H$ are Hopf quasigroups such that their
antipodes are isomorphisms, a Hopf quasigroup $X$ admits a factorization as
$X=AH$ iff $X$ is isomorphic to a double cross product $A\bowtie H$ as Hopf
quasigroups.
