The Fourier Neural Operator (FNO) is a learning-based method for efficiently simulating partial differential equations. We propose the Factorized Fourier Neural Operator (F-FNO) that allows much better generalization with deeper networks. With a careful combination of the Fourier factorization, weight sharing, the Markov property, and residual connections, F-FNOs achieve a six-fold reduction in error on the most turbulent setting of the Navier-Stokes benchmark dataset. We show that our model maintains an error rate of 2% while still running an order of magnitude faster than a numerical solver, even when the problem setting is extended to include additional contexts such as viscosity and time-varying forces. This enables the same pretrained neural network to model vastly different conditions.