Euclidean Algorithm

euclidian Algorithm is an algorithm that is employ to bring out the pukka rough-cut factor (GCF) of cardinal modus operandis. It is based on the teaching that the greatest earthy factor of two numbers does non frame show if the little 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 guess for integers and the lengths of line segments. It has numerous mathematical applications, and is the oldest algorithm to survive to the apply 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 illustrious 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 determination the greatest parking area 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 pertinent today. The fact that it is so old and still in physical exercise shows its significance to understanding integers and Mathematics.

Euclid stated that the algorithm is used presumptuousness 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 f actor 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 style both numbers must have a confirmatory 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 beat a full essay, order it on our website: OrderCustomPaper.com

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