My purpose for using factor analysis is to obtain a small number of factors, which account for most of the variability in the 117 variables. I have extracted 16 factors. These 16 factors have eigenvalues greater than 1.0. Together they account for 81.11% of the variability in the original data.
There is a little difference between factor analysis and extracting number of variables among a larger number of variables. You can simply use PCA for this purpose. But Factor analysis is a derivative of PCA with a grouping phase which done with rotation (Commonly using varimax method) of the axis. When determinant of the correlation matrix is zero you should test the singularity of the matrix, which in turn, lead to some different methods of variable selection. Chick if you don't have Communality more than 1.
See this text for more precise info on Factor analysis.
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