In this paper, we present a general approach to the construction of conservation laws for nonlinear non-holonomic dynamical systems by finding corresponding int egrating factors. The definition of integrating factors for the Routh equations of non-holonomic systems is given, and the necessary conditions for the existenc e of conserved quantities of the non-holonomic dynamical systems are studied in detail. The conservation theorem and its inverse for the systems are established , and an example is given to illustrate the application of the results.