Other Number Systems
As described above, the Euclidean algorithm is used to find the greatest common divisor of two natural numbers (positive integers). However, it may be generalized to the real numbers, and to more exotic number systems such as polynomials, quadratic integers and Hurwitz quaternions. In the latter cases, the Euclidean algorithm is used to demonstrate the crucial property of unique factorization, i.e., that such numbers can be factored uniquely into irreducible elements, the counterparts of prime numbers. Unique factorization is essential to many proofs of number theory.
Read more about this topic: Euclidean Algorithm
Famous quotes containing the words number and/or systems:
“But however the forms of family life have changed and the number expanded, the role of the family has remained constant and it continues to be the major institution through which children pass en route to adulthood.”
—Bernice Weissbourd (20th century)
“In all systems of theology the devil figures as a male person.... Yes, it is women who keep the church going.”
—Don Marquis (1878–1937)