Gibbs Paradox in Grand Canonical Ensemble

Boltzmann Correction Factor (BCF) N! is used in Micro Canonical Ensemble (MCE) and Canonical Ensemble (CE) as a dividing term to reduce the over counting of the states while finding the number of states and partition function. For Grand Canonical Ensemble the indistinguishability was taken into account while deriving the Partition Function (PF) and hence generally the BCF doesn't appear for GCE. We show here that BCF comes as a multiplying factor for harmonic oscillators in GCE for entropy to be extensive.