On a factorization of homeomorphisms of the circle possessing periodic points

We prove that for every orientation-preserving homeomorphism F:S1→S1 possessing periodic points of order n there exist a homeomorphism T:S1→S1 such that Tn=id and a homeomorphism G:S1→S1 without periodic points except fixed points such thatF=Tq○G for an integer 1⩽q