A General Algorithm For Factorization
N. A. Draim · Mathematics Teacher Learning and Teaching PK-12 · 1973
The determination of the primeness or compositeness of an integer is useful in arithmetic for simplifying rational fractions. obtaining an understanding of the arithmetical structure of particular integers, and aiding in calculations relating to the theory of numbers. Numerous special tests have been devised for determining divisibility by special divisors such as 2, 3, 6, 7, 9, and 11. However, a general algorithm for testing any number for its factors, in ascending order of magnitude, does exist and is the subject of this paper. The algorithm is a repeated division process with the successive divisions linked together by the rules of the algorithm. It is amenable to programming for computer factorization and, in fact, has been so used. It reduces the size of the number under test to one-nth its original size after division by n, thus making a significant reduction in the amount of calculation involved and imposing less burden on the storage banks of the computer.