Taylor orientation factors for strain hardening in textured and random polycrystals of magnesium were derived from the ratio of the strain hardening rates of polycrystals to that of single crystals deforming by equivalent polyslip. For polycrystals with textures that inhibit basal and prismatic slip while favouring pyramidal polyslip, the Taylor factor is estimated to be between 2.1 and 2.5, increasing to about 4.5 for randomly textured polycrystals. The micromechanics of strain hardening in polycrystals are discussed.