Euclidean Algorithm

euclidian Algorithm is an algorithm that is employ to keep an eye on the passkey rough-cut factor (GCF) of cardinal modus operandis. It is based on the principle that the sterling(prenominal) greens factor of cardinal numbers does non diversity 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 mull over for integers and the lengths of line segments. It has numerous mathematical applications, and is the oldest algorithm to survive to the manifest 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 storeyed mathematical work was the Elements. It is a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the prop ositions (Robertson). It is in this book that he explains his algorithm for purpose the greatest familiar 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 relevant today. The fact that it is so old and still in intent shows its significance to understanding integers and Mathematics.

Euclid stated that the algorithm is used attached 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 means both numbers must have a electropositive 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 bunk a full essay, order it on our website: OrderCustomPaper.com

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