# Common factor

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Related to common divisor: gcd

## Common factor

An element of return that influences many assets. According to multiple factor risk models, the factors determine correlations between asset returns. Common factors include size (often measured by market capitalization), valuation measures such as price to book value ratio and dividend yield, industries and risk indices.
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If a & b are both even, GCD (a, b) = 2 * GCD (a/2, b/2) because 2 is a common divisor. Multiplication with 2 can be done with bitwise shift operator.
In mathematics, the greatest common divisor (gcd) of two or more integers is the largest positive integer that divides the numbers without a remainder.
where [d.sub.o](z) =1 by definition and [d.sub.i](z) is the monic greatest common divisor of all minors of order i in D(z), i=1,2,.....m.
So if g is the greatest common divisor of the [[alpha].sub.i] (which can be computed in polynomial time), and [alpha]/g = [[[alpha].sub.1]/g, [[alpha].sub.2]/g, ..., [[alpha].sub.N+1]/g] the formula E([alpha])(gt) = E([alpha]/g)(t) holds, and we may assume that the numbers [[alpha].sub.i] span Z without changing the complexity of the problem.
where [[delta].sub.n] is a common divisor of [p.sub.1,n],...,[p.sub.s,n].
Figure 4: The first seven members of the aliquot sequence of 30: sum of proper integer proper divisors divisors 30 1, 2, 3, 5, 6, 10, 15 42 42 1, 2, 3, 6, 7, 14, 21 54 54 1, 2, 3, 6, 9, 18, 27 66 66 1, 2, 3, 6, 11, 22, 33 78 78 1, 2, 3, 6, 13, 26, 39 90 90 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 144 45 144 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 259 24, 36, 48, 72 What is striking about the sequence {30, 42, 54, 66, 78, 90, 144} is that the Greatest Common Divisor (CGD) for its 7 members is 6, which is a 'perfect number' because it equals the sum of its proper divisors (1+2+3=6).
In Section 3, we discuss the concept of the greatest common divisors in the semimodules and show that for any Euclidean semimodule A in which every cyclic subsemimodule is subtractive, then every nonempty finite subset of A has a greatest common divisor.
"Algorithm," she reads, "a set of rules for solving a problem in a finite number of steps, as for finding the greatest common divisor."
Theorem 1 If c = a + b and d = gcd(a, b) the orbit of the billiard ball (on the corresponding table) passes through a lattice point (x, y) on the boundary if and only if d|x and d|y (gcd(a, b) denotes the greatest common divisor of a and b)
Second, the "ideal" district size is used as a common divisor for the population of each state, yielding what are called the states' quotas of Representatives.

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