The radial equation for the hydrogen atom problem is factored to yield raising and lowering operators for the oribtal angular momentum quantum numberl. This procedure, which is a direct analog for the usual treatment of the angular momentum operators, is considered to offer many pedagogical advantages for an introductory course in quantum mechanics over the usual series method of solution. The raising process is terminated by establishing the existence of an upper bound forl. The use of the hypervirial relations is advocated for displaying such an a priori upper bound.