Euclidean Algorithm

euclidean Algorithm is an algorithm that is employ to scrape the transcendent rough-cut factor (GCF) of deuce modus operandis. It is based on the order that the superior leafy ve bulgeable factor of devil numbers does non mannequin show if the littler number is subtracted from the larger number. It was developed by the Greek Mathematician Euclid, and described in his book the Elements. In Elements it is conjecture for integers and the lengths of line segments. It has numerous mathematical applications, and is the oldest algorithm to survive to the try day. Euclids algorithm contributed to understanding of the number theory, and helped prove umteen other theories and identities. Euclid of Alexandria was a Greek Mathematician during the reign of Ptolemy (OConnor). His most renowned mathematical work was the Elements. It is a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions (Rober tson). It is in this book that he explains his algorithm for determination the greatest frequent ingredient of two numbers. He explains that this only applies to numbers that are non premier(a). The algorithm was an important part to understanding integers and is still germane(predicate) today. The fact that it is so old and still in expend shows its significance to understanding integers and Mathematics. Euclid stated that the algorithm is used disposed two numbers not prime to single another, to find their greatest common measure (Euclid). It is a rear of rules for finding the greatest common factor or divisor of two numbers in a finite number of steps. To start, the two numbers that you are looking for cannot be prime numbers. This elbow room both numbers must have a exacting divisor other than 1 and themselves. If they are not the greatest common divisor will always be 1. The Euclidean algorithm is based on the principle that the greatest common divisor of two num bers does not change if the smaller number i! s subtracted from the larger number (Bogomolny). Therefore the first...If you inadequacy to get a full essay, order it on our website: OrderCustomPaper.com

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