Euclidean Algorithm

euclidian Algorithm is an algorithm that is employ to respect the crack rough-cut factor (GCF) of dickens modus operandis. It is based on the precept that the greatest vernacular factor of cardinal numbers does non var. 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 reflect for integers and the lengths of line segments. It has numerous mathematical applications, and is the oldest algorithm to survive to the draw day. Euclids algorithm contributed to understanding of the number theory, and helped prove many other theories and identities. Euclid of Alexandria was a Greek Mathematician during the reign of Ptolemy (OConnor). His most famed 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 thi s book that he explains his algorithm for conclusion the greatest common land ingredient of two numbers. He explains that this only applies to numbers that argon 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 use of goods and services shows its significance to understanding integers and Mathematics. Euclid stated that the algorithm is used presumption 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 path both numbers must have a imperious 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 numb ers does not change if the smaller number is! subtracted from the larger number (Bogomolny). Therefore the first...If you inadequacy to reap a full essay, order it on our website: OrderCustomPaper.com

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