Based on a sample of $(1310.6 pm 7.0) times 10^6~J/psi$ events collected with the BESIII detector, we present measurements of $J/psi$ and $eta^prime$ absolute branching fractions using the process $J/psirightarrowgammaeta^prime$. By analyzing events where the radiative photon converts into an $e^+e^-$ pair, the branching fraction for $J/psi rightarrow gamma eta^prime$ is measured to be $(5.27pm0.03pm0.05)times 10^{-3}$. The absolute branching fractions of the five dominant decay channels of the $eta^prime$ are then measured independently for the first time and are determined to be $mathcal{B}(eta^prime rightarrow gamma pi^{+} pi^{-})$ = (29.90$pm$0.03$pm$0.55)%, $mathcal{B}(eta^prime rightarrow eta pi^{+} pi^{-})$ = (41.24$pm$0.08$pm$1.24)%, $mathcal{B}(eta^prime rightarrow eta pi^{0} pi^{0})$ = (21.36$pm$0.10$pm$0.92)%, $mathcal{B}(eta^prime rightarrow gamma omega)$ = (2.489$pm$0.018$pm$0.074)%, and $mathcal{B}(eta^prime rightarrow gamma gamma)$ = (2.331$pm$0.012$pm$0.035)%, where the first uncertainties are statistical and the second systematic.
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