**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

### Other articles related to "other number systems, number, numbers":

**Other Number Systems**- Noncommutative Rings

... of the remainder ρ0 must be strictly smaller than β, and there must be only a finite

**number**of possible sizes for ρ0, so that the algorithm is guaranteed to terminate ... Most of the results for the GCD carry over to noncommutative

**numbers**... In other words, there are

**numbers**σ and τ such that Γright = σα + τβ The analogous identity for the left GCD is nearly the same Γleft = ασ + βτ Béz ...

39 is the smallest natural

**number**which has three partitions into three parts which all give the same product when multiplied {25, 8, 6}, {24, 10, 5}, {20, 15, 4} ... The thirteenth Perrin

**number**is 39, which comes after 17, 22, 29 (it is the sum of the first two mentioned) ... factor of 392 + 1 = 1522 is 761, which is obviously more than 39 twice, 39 is a Størmer

**number**...

496 is most notable for being a perfect

**number**, and one of the earliest

**numbers**to be recognized as such ... As a perfect

**number**, it is tied to the Mersenne prime 31, 25 - 1, with 24 ( 25 - 1 ) yielding 496 ... Also related to its being a perfect

**number**, 496 is a harmonic divisor

**number**, since the

**number**of proper divisors of 496 divided by the sum of the reciprocals of its divisors, 1, 2, 4, 8 ...

... This article discusses the

**number**thirty-eight ... disambiguation) ← 39 ... → 38 ← 39 ... → List of

**numbers**— Integers 90 ... → Cardinal thirty-eight Ordinal 38th (thirty-eighth ...

... with their first, "'39" does in fact fall in the thirty-ninth position The retired jersey

**number**of former baseball player Roy Campanella The book series "The 39 ... History The

**number**of signers to the United States Constitution, out of 55 members of the Philadelphia Convention delegates The traditional

**number**of times citizens ... Japanese Internet chat slang for "thank you" when written with

**numbers**(3=san 9=kyu) Pier 39 in San Francisco The

**number**of the French department Jura In Afghanistan, the

**number**39 is considered unlucky ...

### Famous quotes containing the words systems and/or number:

“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)

“In this world, which is so plainly the antechamber of another, there are no happy men. The true division of humanity is between those who live in light and those who live in darkness. Our aim must be to diminish the *number* of the latter and increase the *number* of the former. That is why we demand education and knowledge.”

—Victor Hugo (1802–1885)