# common divisor

## Definitions

• WordNet 3.6
• n common divisor an integer that divides two (or more) other integers evenly
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Webster's Revised Unabridged Dictionary
• Common divisor (Math) a number or quantity that divides two or more numbers or quantities without a remainder; a common measure.
• Common divisor (Math) See under Common a.
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## Usage

### In literature:

This common divisor he found to be 1/1440 of a dollar, or 1/1600 the crown sterling.
"Memoir, Correspondence, And Miscellanies, From The Papers Of Thomas Jefferson" by Thomas Jefferson
It took the mind off the finding of the Greatest Common Divisor.
"Emmy Lou" by George Madden Martin
The Executive is the greatest common divisor of a diverse society.
"Behind the Mirrors" by Clinton W. Gilbert
The reader probably never has had occasion to compute a greatest common divisor since he left school.
"The Psychology of Arithmetic" by Edward L. Thorndike
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### In science:

Also, we will always identify the greatest common divisor in A of a number of polynomials by the monic generator of the principal ideal of A generated by them.
Equidistribution for torsion points of a Drinfeld module
Given a set of n distinct points in general position in 2, there are no curves of Taking again common divisors to elements in each row one gets that det Hr,n (e) i=0 (cid:0) e+i r−n+i(cid:1).
Limit linear systems and applications
Let k and n be two positive integers such that u = (k, d) (the greater common divisor between k and n) and d = u · m.
Factorization formulas for Macdonald polynomials
Karmarka N., and Lakshman Y. N., Approximate polynomial greatest common divisors and nearest singular polynomials.
Obtaining Exact Value by Approximate Computations
For positive codimension determinants it will be useful if Λ supports a greatest common divisor function, written gcd. A good reference for this is [As].
New Invariants of Long Virtual Knots
The ring C[t, t−1 ] has greatest common divisors, see [CF].
New Invariants of Long Virtual Knots
If P is square then det(0) η (P ) is deﬁned even if Λ does not possess greatest common divisors.
New Invariants of Long Virtual Knots
The Alexander polynomial, ∆φ, is deﬁned to be the greatest common divisor of the elements of the ﬁrst elementary ideal of Aφ .
On knot Floer homology for some fibered knots
For all λ ∈ IN let gλ be the greatest common divisor of the n-minors of Aλ and let g ′ be the greatest common divisor of the n-minors of A′ .
On binomial set-theoretic complete intersections in characteristic p
Clearly, any pair of two meromorphic functions whose divisors have no common points is admissible (we call such pairs generic).
The resultant on compact Riemann surfaces
In a different context, the subresultants are determinants of certain submatrices of the Sylvester matrix (12) which occur as successive remainders in ﬁnding the greatest common divisor of two polynomials by the Euclid algorithm .
The resultant on compact Riemann surfaces
K (K ′ ) are the complete elliptic integrals of the ﬁrst kind of modulus k (k ′ ) and L0, m10 and m20 are integers whose greatest common divisor is one.
New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity
The situation has a good deal in common with the Dirichlet divisor and the Gaussian circle problems.
A lower bound for the error term in Weyl's law for certain Heisenberg manifolds
By (k, l) we denote the greatest common divisor of k and l.
The ternary Goldbach problem with primes from arithmetic progressions
Let X be a simple normal crossing divisor on a smooth variety M and let D be an Rdivisor on M such that Supp(D + X ) is simple normal crossing and that D and X have no common irreducible components.
Introduction to the log minimal model program for log canonical pairs
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