Euclidean Algorithm

euclidian Algorithm is an algorithm that is employ to recover the original rough-cut factor (GCF) of twain modus operandis. It is based on the teaching that the superior greennessalty factor of ii numbers does non mix 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 imagine for integers and the lengths of line segments. It has numerous mathematical applications, and is the oldest algorithm to survive to the show up day. Euclids algorithm contributed to understanding of the number theory, and helped prove umpteen other theories and identities. Euclid of Alexandria was a Greek Mathematician during the reign of Ptolemy (OConnor). His most historied mathematical work was the Elements. It is a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions (Robertson). It is in this book that he explains his algorithm for determination the greatest common ingredient of two numbers. He explains that this only applies to numbers that atomic number 18 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 lend oneself shows its significance to understanding integers and Mathematics.

Euclid stated that the algorithm is used minded(p) 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 di visor of two numbers in a finite number of s! teps. To start, the two numbers that you are looking for cannot be prime numbers. This substance both numbers must have a appointed 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 numbers does not change if the smaller number is subtracted from the larger number (Bogomolny). Therefore the first...If you inadequacy to perplex a full essay, order it on our website: OrderCustomPaper.com

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