a tracial von neumann algebra $m$ is called prime if it cannot be decomposed as the tensor product of two nontrivial (not type ${\rm i}$) subalgebras. naturally, if $m$ is not prime, one asks if $m$ can be uniquely factored as a tensor product of prime subalgebras. the first result in this direction is due to ozawa and popa in 2003, who gave a large class of groups $\mathcal{c}$ such that for any $\gamma_1, \dots, \gamma_n \in \mathcal{c}$, the associated von neumann algebra $l(\gamma_1) \otimes \cdots \otimes l(\gamma_n)$ is uniquely factored. this talk will focus on von neumann algebras arising from a class of measured equivalence relations, and how the techniques of ozawa and popa can be adapted to this setting.