The centrality dependence of the midrapidity charged particle multiplicity in Au+Au heavy-ion collisions at sqrt[SNN]=19.6 and 200 GeV is presented. Within a simple model, the fraction of hard (scaling with number of binary collisions) to soft (scaling with number of participant pairs) interactions is consistent with a value of x=0.13±0.01(stat)±0. 05(syst) at both energies. The experimental results at both energies, scaled by inelastic p(p̄)+p collision data, agree within systematic errors. The ratio of the data was found not to depend on centrality over the studied range and yields a simple linear scale factor of R200/19.6=2.03±0. 02(stat) ±0.05(syst).