We investigate the minimal number of failures that can *partition* a system where processes communicate both through shared memory and by message passing. We prove that this number precisely captures the resilience that can be achieved by algorithms that implement a variety of shared objects, like registers, and solve common tasks, like randomized consensus, approximate agreement and renaming. This has implications for the m&m-model of Aguilera et al., and for the hybrid, cluster-based model of Imbs and Raynal.