ozawa and popa proved a unique factorization property for tensor products of free group factors. roughly speaking, this means these tensor products "remember" each tensor component. in this seminar, we study similar factorization results for free quantum group factors. in the proof, we use a condition (ao) type phenomena for continuous cores of the tensor products, and prove first a weak factorization property on the cores. then we deduce the desired property for the original tensor products.