1520s, from Latin efficacia "efficacy, efficiency," from efficax (genitive efficacis) "powerful, effectual, efficient," from stem of efficere "work out, accomplish" (see effect (n.)). Earlier in same sense was efficace (c. 1200), from Old French eficace (14c.), from Latin efficacia; also efficacite (early 15c.), from Latin efficacitatem.
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