  The factorization technique for superintegrable Hamiltonian systems is
revisited and applied in order to obtain additional (higher-order) constants of
the motion. In particular, the factorization approach to the classical
anisotropic oscillator on the Euclidean plane is reviewed, and new classical
(super)integrable anisotropic oscillators on the sphere are constructed. The
Tremblay-Turbiner-Winternitz system on the Euclidean plane is also studied from
this viewpoint.
