Separability in Petri nets means the property for a net k *N with an initial marking k *M to behave in the same way as k parallel instances of the same net N with an initial marking M, thus divided by k. We prove the separability of plain, bounded, reversible and persistent Petri nets, a class of nets that extends the well-known live and bounded marked graphs. We establish first a weak form of separability, already known to hold for marked graphs, in which every firing sequence of k * N is simulated by a firing sequence of k parallel instances of N with an identical firing count. We establish on top of this a strong form of separability, in which every firing sequence of k * N is simulated by an identical firing sequence of k parallel instances of N.