Using a sample of 106 million ψ(3686) decays, the branching fractions of ψ(3686)→γχc0,ψ(3686)→γχc1, and ψ(3686)→γχc2 are measured with improved precision to be (9.389±0.014±0.332)%, (9.905±0.011±0.353)%, and (9.621±0.013±0.272)%, respectively, where the first uncertainties are statistical and the second ones are systematic. The product branching fractions of ψ(3686)→γχc1,χc1→γJ/ψ and ψ(3686)→γχc2,χc2→γJ/ψ and the branching fractions of χc1→γJ/ψ and χc2→γJ/ψ are also presented.