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This book investigates three computer algorithms that attempt to find factors of a number. If the number has no factors, then it is prime. The first algorithm does not use any table of prime numbers nor does it perform any standard division, yet it finds factors with great efficiency. The second algorithm runs through a series of consecutive odd numbers looking for a solution. This is an example of the worst approach. The third algorithm uses a unique approach too involved to explain here. Its efficiency varies depending on the number itself and the list of prime numbers used in the analysis. The first algorithm has two variants, one of which could be very useful. A fourth program using the method of trial division is included for comparison.