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We characterize protostellar multiplicity in the Orion molecular clouds usingALMA 0.87~mm and VLA 9~mm continuum surveys toward 328 protostars. Theseobservations are sensitive to projected spatial separations as small as$\sim$20~au, and we consider source separations up to 10$^4$~au as potentialcompanions. The overall multiplicity fraction (MF) and companion fraction (CF)for the Orion protostars are 0.30$\pm$0.03 and 0.44$\pm$0.03, respectively,considering separations from 20 to 10$^4$~au. The MFs and CFs are corrected forpotential contamination by unassociated young stars using a probabilisticscheme based on the surface density of young stars around each protostar. Thecompanion separation distribution as a whole is double peaked and inconsistentwith the separation distribution of solar-type field stars, while theseparation distribution of Flat Spectrum protostars is consistent solar-typefield stars. The multiplicity statistics and companion separation distributionsof the Perseus star-forming region are consistent with those of Orion. Based onthe observed peaks in the Class 0 separations at $\sim$100~au and$\sim$10$^3$~au, we argue that multiples with separations $<$500~au are likelyproduced by both disk fragmentation and turbulent fragmentation with migration,and those at $\ga$10$^3$~au result primarily from turbulent fragmentation. Wealso find that MFs/CFs may rise from Class 0 to Flat Spectrum protostarsbetween 100 and 10$^3$~au in regions of high YSO density. This finding may beevidence for migration of companions from $>$10$^3$~au to $<$10$^3$~au, andthat some companions between 10$^3$ and 10$^4$~au must be (or become) unbound.

The VLA/ALMA Nascent Disk and Multiplicity (VANDAM) Survey of Orion Protostars V. A Characterization of Protostellar Multiplicity