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We establish necessary and sufficient conditions for the existence offactorizable steady states of the Generalized Zero Range Process. This processallows transitions from a site $i$ to a site $i+q$ involving multiple particleswith rates depending on the content of the site $i$, the direction $q$ ofmovement, and the number of particles moving. We also show the sufficiency of asimilar condition for the continuous time Mass Transport Process, where themass at each site and the amount transferred in each transition are continuousvariables; we conjecture that this is also a necessary condition.Comment: 9 pages, LaTeX with IOP style files. v2 has minor corrections; v3 has  been rewritten for greater clarit

Product measure steady states of generalized zero range processes