We propose a generalized method of variable selection, which is applied for the case, in which the number of the criterion variables exceeds two. By using the method, we can select criterion variables as well as explanatory variables simultaneously in canonical correlation analysis, using the G.C.D Generalized Coefficient of Determination as a maximization criterion. Furthermore, the generalized method of variable selection can be applied to factor analysis, in which case forward selection method is also performed to real variables, with the number of latent factor variables as fixed. Finally, we show two numerical examples demonstrating the validity of our procedure.