Gauss-Seidel computing procedures have previously been used to obtain Maximum Likelihood and Minres factor analytic solutions. This paper is concerned with the use of Gauss-Seidel computing procedures to obtain five solutions: Maximum Likelihood, Minres, Alpha and two recently derived weighted least squares solutions. The treatment of negative residual variances is considered, modifications of approaches suggested by Harman and Fukuda (1966) and by Joreskog (1967a) being used. Three "generalized characteristic value" problems occur and procedures for solving them are provided. Finally, examples of the application of the Gauss-Seidel procedures are given and are used to illustrate properties of the five factor analytic solutions.