Euclidean Algorithm

euclidian Algorithm is an algorithm that is employ to examine the pukka rough-cut factor (GCF) of deuce modus operandis. It is based on the education that the greatest plebeian factor of 2 numbers does non smorgasbord show if the smaller 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 shit 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 famous 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 conclusion the greatest coarse 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 relevant today. The fact that it is so old and still in economic consumption shows its significance to understanding integers and Mathematics.

Euclid stated that the algorithm is used given over 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 numbe rs in a finite number of steps. To start, th! e two numbers that you are looking for cannot be prime numbers. This gist both numbers must have a authoritative 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 farm a full essay, order it on our website: OrderCustomPaper.com

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