This paper give a definition of edge matrix and cycle coloring with complete graph , and also a construction of the theorem for n Hamilton. Clarify the basic ideas of 2-factorizations with complete graph, and proof the theorem of 2-factorization. After that, we show the whole process of the complete graphs 2-factorization for K10 and K17, when it is that n=5 and n=8. We obtain the edge matrix of the K17 and edge sets for 8 Hamilton. Finally, it can be test and verify the construction of theorem with n Hamilton, and theorem of 2-factorizations is a simple and feasible effectiveness method.