Factor analysis followed by cluster analysis ( time sensitive)

Hi everyone,

I have done a principal component analysis using SPSS and now have 3 components.
2 components have 4 items in the sub scale and 1 component has 3 items. Component scores using regression for each factor was added as variables to the data set by SPSS.

My question is: can the component scores be used as the variables for K-means cluster analysis to form clusters? My aim is to find out the exact number of cases in each factor, which I intend to do through cluster analysis. is this the statistically correct method?

Thank you for any input.