We introduce a high-capacity associative memory capable of factorizing compositional representations of variables. The proposed approach is implemented as a continuous-time oscillator neural network. By performing factorization with a continuous-time dynamical system, the proposed Factorizing Oscillator Associative Memory (FOAM) provides efficient solutions to computationally hard problems such as inference in compositional representations and combinatorial optimization. We demonstrate favorable performance compared to existing approaches to factorization, improved interpretability, and relevance to standard tasks such as the subset sum problem.