We have measured transverse momentum distributions of charged hadrons produced in Au+Au collisions at sqrt[s(NN)]=62.4 GeV. The spectra are presented for transverse momenta 0.25<p(T)<4.5 GeV/c, in a pseudorapidity range of 0.2<eta<1.4. The nuclear modification factor R(AA) is calculated relative to p+p data at the same collision energy as a function of collision centrality. For 2<p(T)<4.5 GeV/c, R(AA) is found to be significantly larger than in Au+Au collisions at sqrt[s(NN)]= 130 and 200 GeV. In contrast to the large change in R(AA), we observe a very similar centrality evolution of the p(T) spectra at sqrt[s(NN)]=62.4 and 200 GeV. The dynamical origin of this surprising factorization of energy and centrality dependence of particle production in heavy-ion collisions remains to be understood.