  We investigate the possibility and conditions to factorize the entanglement
evolution of a multiqubit system passing through multi-sided noisy channels. By
means of a lower bound of concurrence (LBC) as entanglement measure, we derive
an explicit formula of LBC evolution of the N-qubit generalized
Greenberger-Horne-Zeilinger (GGHZ) state under some typical noisy channels,
based on which two kinds of factorizing conditions for the LBC evolution are
presented. In this case, the time-dependent LBC can be determined by a product
of initial LBC of the system and the LBC evolution of a maximally entangled
GGHZ state under the same multi-sided noisy channels. We analyze the realistic
situations where these two kinds of factorizing conditions can be satisfied. In
addition, we also discuss the dependence of entanglement robustness on the
number of the qubits and that of the noisy channels.
