  We discover a simple factorization law describing how multipartite
entanglement of a composite quantum system evolves when one of the subsystems
undergoes an arbitrary physical process. This multipartite entanglement decay
is determined uniquely by a single factor we call the entanglement resilient
factor (ERF). Since the ERF is a function of the quantum channel alone, we find
that multipartite entanglement evolves in exactly the same way as bipartite
(two qudits) entanglement. For the two qubits case, our factorization law
reduces to the main result of Nature Physics 4, 99 (2008). In addition, for a
permutation $P$, we provide an operational definition of $P$-asymmetry of
entanglement, and find the conditions when a permuted version of a state can be
achieved by local means.
