The demand for stable isotopes in physical and chemical research and in medical diagnostics is growing, and the gas centrifuge process is able to provide large quantities of stable isotopes. A set of diffusion equations describing separation in a gas centrifuge for a multicomponent mixture is established. These equations involve general diffusion coefficients. Using the radial averaging method and the simplified diffusion transport vector for a multicomponent isotopic mixture, nonlinear partial differential equations are transformed to a set of nonlinear ordinary differential equations. An iteration method for the solution is presented. The relationship between the separation factor and the mass difference, gamma(ij) = gamma(O)(Mj-Mi), is shown to be in agreement with both the computational and the experimental results with very high precision.