The GRAPES-3 experiment, located in Ooty, India, consists of a densely packed array of $\sim$400 plastic scintillator detectors and a large area (560 $m^2$) muon telescope. The muons produced in extensive air showers (EAS) are key observables for analyzing the primary cosmic ray composition. The GRAPES-3 muon telescope (G3MT) measures the muonic component in the EASs by counting the reconstructed muon tracks based on the proportional counter hit information. An extensive simulation study of EASs is required to explore the properties of cosmic ray muons.However, the persistent discrepancies between the hadronic interaction models and experimental data at higher energies highlight the need for further investigation of the current models in use. Our comparative analysis of muon multiplicity predictions from 100 TeV, 500 TeV and 1 PeV monoenergetic vertical showers, considering proton, helium, nitrogen, aluminum, and iron primaries, shows that the percentage difference among QGSJET II-04, SIBYLL 2.3d, and EPOS-LHC models is within 5% at 100 TeV and decreases at higher energies. In these proceedings, we present a detailed study of the Muon Multiplicity Distributions (MMDs) for proton and iron primaries at different energies. We further compare the predictions of different hadronic interaction models across various primaries by analyzing the mean kinetic energy and the corresponding number of muons as functions of primary mass. In addition we also report the preliminary results of MMDs of Gaisser Stanev Tilav (GST) composition model and compared it with the GRAPES-3 data.