Euclidean Algorithm

euclidean Algorithm is an algorithm that is employ to bugger off the higher-ranking rough-cut factor (GCF) of cardinal modus operandis. It is based on the principle that the greatest crude factor of deuce numbers does non transition 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 reckon for integers and the lengths of line segments. It has numerous mathematical applications, and is the oldest algorithm to survive to the nominate 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 far-famed mathematical work was the Elements. It is a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions (Rob ertson). It is in this book that he explains his algorithm for conclusion the greatest communal 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 subroutine shows its significance to understanding integers and Mathematics.

Euclid stated that the algorithm is used wedded 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 o r 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 inwardness both numbers must have a lordly 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 bring in a full essay, order it on our website: OrderCustomPaper.com

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