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Topic: Divisor

Related Topics

greatest common divisor

zero divisors

harmonic divisor number

Table of divisors

linear system of divisors

Cartier divisor

proper divisor

Weil divisor

canonical divisor

unitary divisor

Effective divisor

elementary divisor

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	The Prime Glossary: divisor (Site not responding. Last check: 2007-10-21)
		The divisors (or factors) of a positive integer are the integers that evenly divide it.
		The proper divisors of 27 are 1, 3 and 9.
		There is another use of the word divisor: when we divide an integer a by a non-zero integer b, to get a quotient and remainder (see the division algorithm), b is the divisor and a is the dividend.
	primes.utm.edu /glossary/page.php?sort=Divisor (160 words)

	Greatest common divisor - Wikipedia, the free encyclopedia
		In mathematics, the greatest common divisor (gcd), sometimes known as the greatest common factor (gcf) or highest common factor (hcf) of two integers which are not both zero is the largest integer that divides both numbers.
		The greatest common divisor is useful for reducing vulgar fractions to be in lowest terms.
		If d is a common divisor of a and b, and every common divisor of a and b divides d, then d is called a greatest common divisor of a and b.
	en.wikipedia.org /wiki/Greatest_common_divisor (764 words)

	Divisor (Site not responding. Last check: 2007-10-21)
		In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder.
		The positive divisors of 42 are {1, 2, 3, 6, 7, 14, 21, 42}.
		Divisors are a generalization of subvarieties of algebraic varieties; two different generalizations are in common use, Cartier divisors and Weil divisors.
	www.theezine.net /d/divisor.html (587 words)

	Harmonic divisor number - Wikipedia, the free encyclopedia
		A harmonic divisor number, or Ore number, is a number whose divisors, averaged in a harmonic mean, results in an integer.
		Three of these listed are also perfect numbers, and like perfect numbers, harmonic divisor numbers tend to be even numbers, at least in the range observed.
		For example, 496 is a harmonic divisor number because 10, its number of divisors, divided by the sum of the reciprocals of its divisors, 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496, (the harmonic mean), yields an integer, 5 in this case.
	en.wikipedia.org /wiki/Harmonic_divisor_number (160 words)

	Greatest common divisor
		In mathematics, the greatest common divisor (abbreviated GCD), or highest common factor (HCF) of two integers which are not both zero is the largest integer that divides both numbers.
		The greatest common divisor of a and b (not both zero) may be defined alternatively and equivalently as follows: it is the smallest positive integer d which can be written in the form ap+bq where p and q are integers.
		If c is a common divisor of a and b, and every common divisor of a and b divides c, then c is called a greatest common divisor of a and b.
	www.wordlookup.net /gr/greatest-common-divisor.html (655 words)

	► » "Divisor-Sum Cycles" (Site not responding. Last check: 2007-10-21)
		Note: The divisor of a(k), that is part of the sum equal to a(k+1),
		Note: The divisor of a(k), that is part of the sum equal to =
		divisor of a(k-1) is less than or equal to (2m+1)/3 which is less than
	www.science-chat.org /Divisor-Sum-Cycles-5411540.html (1633 words)

	PlanetMath: divisor
		This is version 3 of divisor, born on 2001-12-12, modified 2002-09-23.
		The definition of (Weil) Divisor seems a bit too specialized here, at least from an algebraic geometer's point of view.
		I think the more general definition of a divisor as an element of the free abelian group generated by the prime divisors would be preferable here (a la Hartshorne).
	planetmath.org /encyclopedia/DivisorOnACurve.html (96 words)

	Math Forum - Ask Dr. Math
		Repeat the process using the divisor as the new dividend and the remainder as the new divisor: 198 = 354 + 36 54 = 136 + 18 36 = 218 + 0 When we get 0 as the remainder, the last divisor*, here 18, is the GCF of the given integers.
		This shows that any common divisor of the first two numbers must also divide the last divisor, by working down the chain of equations one at a time.
		This shows that any factor of the last divisor, including that last divisor itself, also divides both of the first numbers, by working up the chain of equations one step at a time.
	mathforum.org /library/drmath/view/51897.html (438 words)

	[No title]
		Math 405 Constructive Proof of FTA (Fundamental Theorem of Arithmetic) 4 Feb. Construct the prime factors of a positive integer n.
		Each element in factorVec is a prime number and a divisor of n.
		Since a < divisor, part b of the loop invariant is true and so a does not divide currentN.
	www.cbu.edu /~yanushka/m405/n.2 (98 words)

	ABSTRACT ALGEBRA ON LINE: Integers
		In this case we also say that b is a divisor of a, and we use the notation b
		Any two nonzero integers a and b have a greatest common divisor, which can be expressed as the smallest positive linear combination of a and b.
		The greatest common divisor of two numbers can be computed by using a procedure known as the Euclidean algorithm.
	www.math.niu.edu /~beachy/aaol/integers.html (950 words)

	Homework, Sections 8.3 and 8.4, and Supplementary Exercises
		Thus, the common divisors of (18,60) are 1, 2, 3, and 6.
		The common divisors of (18,75) are 1 and 3.
		The common divisors of (60,75) are 1, 3, 5, and 15.
	www.math.fau.edu /Radulescu/mgf1107/hmwk8-3,8-4,pluss.html (1664 words)

	The Anti-Divisor (Site not responding. Last check: 2007-10-21)
		The anti-divisor, or unbiased non-divisor, is a concept related very closely to the concept of prime numbers, and the concept of a divisor.
		A divisor is a combination of these factors, for example 63 has the divisors 1,3,7,9,21 and 63, as 63 divided by any of these numbers yields an integer.
		It logically follows from this that any number that is not a divisor of an integer is a non-divisor.
	www.users.globalnet.co.uk /~perry/maths/antidivisor.htm (804 words)

	"Golden" mirror-symmetrical digit-to-analog converter (DAC)
		It is well known that the resistive divisors with the "binary" ratios are the basis of design of the classical "binary" DAC.
		The equivalent electrical circuits of the divisor are shown in Fig.1-b, c, d.
		Then the equivalent circuit of the divisor regarding to the point C may be presented in the form in Fig 1-d.
	www.goldenmuseum.com /1412GoldenDAC_engl.html (816 words)

	PlanetMath: greatest common divisor
		Given two (rational) integers, one can construct their gcd via Euclidean algorithm.
		Cross-references: divisors, integral domain, commutative ring, Bezout identity, linear combination, Euclidean algorithm, rational, positive, integers
		This is version 11 of greatest common divisor, born on 2001-10-16, modified 2005-09-24.
	planetmath.org /encyclopedia/GreatestCommonDivisor.html (169 words)

	Great Common Divisor (Site not responding. Last check: 2007-10-21)
		of two positive integers a and b, sometimes written (a, b), is the largest divisor common to a and b.
		The greatest common divisor of a and b is implemented in
		The Euclidean algorithm can be used to find the greatest common divisor of two integers.
	www.cs.kent.edu /~yizhou/great_common_divisor.htm (330 words)

	Divisors
		Given a function field F/k and a divisor D belonging to F/k, return a vector space V and a k-linear mapping h: V longrightarrow F such that V is isomorphic to the Riemann-Roch space (L)(D) subset F under h.
		Return the complementary divisor D^# of D. The function field F/k of D must be a finite extension of a rational function field k(x).
		The group of divisor classes is isomorphic to the product of a copy of Z and the group of divisors classes of degree zero which is a finite abelian group.
	www.math.niu.edu /help/math/magmahelp/text710.html (2569 words)

	Two properties of Greatest Common Divisor
		Greatest Common Divisor is one of the best known arithmetic notions.
		In other words, r, an integer smaller than g, would also be representable as a linear combination of a and b which would contradict our assumption that g is the least such integer.
		Note that as + bt = gcd(a,b) implies that any common divisor of a and b also divide gcd(a,b).
	www.cut-the-knot.org /Generalization/gcd.shtml (330 words)

	The Anti-Divisor (Site not responding. Last check: 2007-10-21)
		any number not a divisor or an anti-divisor, is called a k-biased divisor.
		A k-biased divisor is offset around a number by k.
		That is, the difference between the two closest factors of the divisor to n.
	www.users.globalnet.co.uk /~perry/maths/antidivisorother.htm (844 words)

	Divisors
		Testing equality of divisors is often made simpler by having a ``normal form'' for divisors.
		A divisor $D$ is principal iff $L(D)$ has dimension one, and the zero locus of its generator is the empty set.
		We wish to compute homomorphisms from the canonical module into $S_X$, and take the divisor whose first ideal is the image of a homomorphism of non-negative degree, and whose second ideal is an arbitrary nonzero element of $S_X$ whose degree is equal to the degree of the homomorphism.
	www.math.umn.edu /systems_guide/Macaulay2/html/0585.html (2642 words)

	Greatest Common Divisor (Site not responding. Last check: 2007-10-21)
		greatest common divisor definition of greatest common divisor in computing dicti...
		Computing the greatest common divisor of x and y...
		The greatest common divisor and least common multiple...
	www.scienceoxygen.com /math/10.html (127 words)

	Computing primes (jun 99)
		I'm establishing a lexical local variable for this loop, initializing it to 2, and incrementing it by one until it hits 10,000.
		After the prime number '2', there are no further prime numbers that are even, and there is also no reason to try any divisors that are even.
		Similarly, the inner loop tries all odd numbers starting with 3 as potential divisors, but still stopping when the square of the divisor exceeds the candidate prime.
	www.stonehenge.com /merlyn/UnixReview/col26.html (1473 words)

	2 Greatest common divisor (Site not responding. Last check: 2007-10-21)
		We will study three algorithms and their extensions.
		The fundamental question is to find the greatest common divisor or highest common factor d of a pair a, b of integers.
		One also knows that there is a formula ax + by = d and in some applications it is necessary to determine x and y as well.
	www.imsc.ernet.in /~kapil/crypto/notes/node8.html (133 words)

	Dogs of the Dow - Dow Divisor
		To keep historical continuity and allow for a comparison to be made to past Dow values, the editors of the Wall Street Journal modify the index with a Dow divisor.
		The Dow divisor is simply a number which takes stock splits and other market changes into account.
		So in order to calculate the current value of the Dow, one must add up the stock prices of each of the 30 Dow components and divide by 30 and then divide by the Dow divisor.
	www.dogsofthedow.com /Dow_Divisor.htm (230 words)

	Example: Testing for Primality
		Since ancient times, mathematicians have been fascinated by problems concerning prime numbers, and many people have worked on the problem of determining ways to test if numbers are prime.
		One way to test if a number is prime is to find the number's divisors.
		This means that the algorithm need only test divisors between 1 and
	mitpress.mit.edu /sicp/chapter1/node17.html (1830 words)

	HW#2 Greatest Common Divisor System Design (Site not responding. Last check: 2007-10-21)
		Assuming we have 4 pairs of unsigned numbers stored in 8 memory cells(addressed 0-7), upon system_start signal, the GCD system compute the greatest common divisor for each pair of the numbers and store the result back into the second cell.
		After all 4 pairs are calculated, the system_done signal are raised high to imform that the computation is done.(just for practice.)
		The 3-bit address are connected to the memory which will decode the address to select a memory cell, and when Q0, Q1 Q2 are high, addr_full will be raised high and fed to the control unit.
	www.ee.pdx.edu /~xiang/ee510vh/code/report/prj2rep.html (432 words)

	[No title]
		virtual boundexpr simplify(bizarre_bounds_info b, int divisor); virtual boolean divisible_by(int div,int do_division); virtual operand gen(block_symtab scope); // mnok = 0: mn is meaningless, mnok = 1: exact, mnok = 2: mn only a bound ************ * 142,148 **** mn_boundexpr():mns(0){} ~mn_boundexpr(); operand gen(block_symtab *scope); !
		boundexpr simplify(bizarre_bounds_info b, int divisor); void replace(tree_for a,access_vector av); mn_type mono(tree_for a,int crash_on_bad); void operator = (int); ************* * 164,170 **** mx_boundexpr():mxs(0){} ~mx_boundexpr(); operand gen(block_symtab *scope); !
		boundexpr simplify(bizarre_bounds_info b, int divisor); void replace(tree_for a,access_vector av); mn_type mono(tree_for a,int crash_on_bad); void operator = (int); ************* * 187,193 **** void range(int mn,int mnok,int mx,int mxok); operand gen(block_symtab *scope); ~av_boundexpr(); !
	suif.stanford.edu /suif/mlists/suif-bugs/199607/19960723.html (929 words)

	Determining the Actual Sample Rate of an Acquisition in NI-DAQmx - KnowledgeBase - Support - National Instruments
		The SamplClk.TimebaseDiv property provides the divisor used to divide down one of the timebase frequencies to achieve your desired sample clock rate.
		For example lets assume the divisor is a 16 bit integer.
		This allows the 20 MHz timebase to be used for all frequencies above 305.18 Hz because a 16-bit integer can yield a divisor of 65,535.
	digital.ni.com /public.nsf/allkb/4BBE1409700F6CE686256E9200652F6B (232 words)

	Finding All Prime Factors of a Positive Integer
		In the above, if Divisor cannot evenly divide Input or Input is 1, we exit the loop.
		The former condition states that Divisor is not a factor of Input, while the latter means Input is 1 and does not have any other factor.
		Since 2 is the only even prime number, we'd better remove all factors of 2 before starting any other work.
	www.cs.mtu.edu /~shene/COURSES/cs201/NOTES/chap04/factor.html (1015 words)

	Homework, Sections 8.3 and 8.4, and Supplementary Exercises (Site not responding. Last check: 2007-10-21)
		For example, 2 is the greatest common divisor of 4 and 6, and, for
		Find the greatest common divisor of 18 and 24.
		Find the greatest common divisor of 206 and 616.
	www.math.fau.edu /htmlfile/outlines/mfla2f00h6.html (247 words)

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