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An algorithm for finding the prime implicants of a Boolean function is given. The algorithm is similar to Nelson's algorithm since both involve the operations of complementing, expanding, and simplifying, but the new algorithm includes the additional operation of factoring. The algorithm with factoring is proved, and it is shown that factoring accounts for a dramatic increase in efficiency over Nelson's algorithm. The increased efficiency is illustrated with timing results obtained from several examples that were implemented for both algorithms using the symbolic manipulation systems SETS.