The computer algebra algorithm developed in this paper is useful in computer-aided geometric reasoning. In particular, certain geometric calculations can be converted into manipulations in the exterior algebra (Grassman algebra). Rewriting these statements to provide a geometric interpretation is more complex, however. By making use of the natural relationship between projective geometry and the Cayley algebra, statements in the exterior algebra can be expressed as Cayley algebra expressions through a process called Cayley factorization. The necessary background on Cayley algebra and the exterior algebra are provided as part of the detailed explanation of the algorithm. Implementation details and open questions are also discussed.