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The collapse and fragmentation of initially prolate and oblate, magneticmolecular clouds is calculated in three dimensions with a gravitational,radiative hydrodynamics code. The code includes magnetic field effects in anapproximate manner: magnetic pressure, tension, braking, and ambipolardiffusion are all modelled. The parameters varied for both the initiallyprolate and oblate clouds are the initial degree of central concentration ofthe radial density profile, the initial angular velocity, and the efficiency ofmagnetic braking (represented by a factor $f_{mb} = 10^{-4}$ or $10^{-3}$). Theoblate cores all collapse to form rings that might be susceptible tofragmentation into multiple systems. The outcome of the collapse of the prolatecores depends strongly on the initial density profile. Prolate cores withcentral densities 20 times higher than their boundary densities collapse andfragment into binary or quadruple systems, whereas cores with central densities100 times higher collapse to form single protostars embedded in bars. Theinclusion of magnetic braking is able to stifle protostellar fragmentation inthe latter set of models, as when identical models were calculated withoutmagnetic braking (Boss 2002), those cores fragmented into binary protostars.These models demonstrate the importance of including magnetic fields in studiesof protostellar collapse and fragmentation, and suggest that even when magneticfields are included, fragmentation into binary and multiple systems remains asa possible outcome of protostellar collapse.

Collapse and Fragmentation of Molecular Cloud Cores. X. Magnetic Braking of Prolate and Oblate Cores