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Integer that divides another integer
In mathematics, a divisor of an integer n , {\displaystyle n,} also called a factor of n , {\displaystyle n,} is an integer m {\displaystyle m} that may
Divisor
Largest integer that divides given integers
In mathematics, the greatest common divisor (GCD), also known as greatest common factor (GCF), of two or more integers, which are not all zero, is the
Greatest_common_divisor
Topics referred to by the same term
A divisor is the second operand of a division. A divisor may also refer to Divisor (number theory), an integer that divides evenly another integer Divisor
Divisor_(disambiguation)
American stock market index composed of 30 industry leaders
the sum of the prices of all thirty stocks divided by a divisor, the Dow Divisor. The divisor is adjusted in case of stock splits, spinoffs or similar
Dow_Jones_Industrial_Average
The lowest common divisor is a term mistakenly used to refer to: Lowest common denominator, the lowest common multiple of the denominators of a set of
Lowest_common_divisor
Arithmetic function related to the divisors of an integer
number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts
Divisor_function
Generalizations of codimension-1 subvarieties of algebraic varieties
divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common use, Cartier divisors
Divisor_(algebraic_geometry)
Ring element that can be multiplied by a nonzero element to equal 0
In abstract algebra, an element a of a ring R is called a left zero divisor if there exists a nonzero x in R such that ax = 0, or equivalently if the
Zero_divisor
In mathematics, the theta divisor Θ is the divisor in the sense of algebraic geometry defined on an abelian variety A over the complex numbers (and principally
Theta_divisor
The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n/m is again an integer (which
Table_of_divisors
Positive integer whose divisors have a harmonic mean that is an integer
harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers
Harmonic_divisor_number
In mathematics, specifically algebraic geometry, an exceptional divisor for a regular map f : X → Y {\displaystyle f:X\rightarrow Y} of varieties is a
Exceptional_divisor
In algebraic geometry, a divisorial scheme is a scheme admitting an ample family of line bundles, as opposed to an ample line bundle. In particular, a
Divisorial_scheme
Number divisible only by 1 and itself
evenly. Every natural number has both 1 and itself as a divisor. If it has any other divisor, it cannot be prime. This leads to an equivalent definition
Prime_number
Arithmetic operation
What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient. At an elementary level the division
Division_(mathematics)
Certain type of divisor of an integer
mathematics, a natural number a is a unitary divisor (or Hall divisor) of a number b if a is a divisor of b and if a and b / a are coprime, having no
Unitary_divisor
Error-detecting code for detecting data changes
the polynomial divisor with the bits above it. The bits not above the divisor are simply copied directly below for that step. The divisor is then shifted
Cyclic_redundancy_check
Summatory function of the divisor-counting function
In number theory, the divisor summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptotic
Divisor_summatory_function
Topics referred to by the same term
least common divisor is a confusion of the following two distinct concepts in arithmetic: Least common multiple Greatest common divisor This disambiguation
Least_common_divisor
{\displaystyle z} of a Banach algebra A {\displaystyle A} is called a topological divisor of zero if there exists a sequence x 1 , x 2 , x 3 , . . . {\displaystyle
Topological_divisor_of_zero
Concept in mathematical ring theory
In mathematics, the notion of a divisor originally arose within the context of arithmetic of whole numbers. With the development of abstract rings, of
Divisibility_(ring_theory)
Esoteric, minimalist programming language
set up divisor (13) for second division loop (MEMORY LAYOUT: zero copy dividend divisor remainder quotient zero zero) >-[>+>>] Reduce divisor; Normal
Brainfuck
Rule for proportional allocation
The highest averages, divisor, or divide-and-round methods are a family of apportionment rules, i.e. algorithms for fair division of seats in a legislature
Highest_averages_method
Algebraic formula
In algebra, the elementary divisors of a module over a principal ideal domain (PID) occur in one form of the structure theorem for finitely generated modules
Elementary_divisors
Relating two numbers and their greatest common divisor
greatest common divisor. The theorem's statement is as follows: Bézout's identity—Let a and b be integers with greatest common divisor d. Then there exist
Bézout's_identity
In mathematics, more specifically general topology, the divisor topology is a specific topology on the set X = { 2 , 3 , 4 , . . . } {\displaystyle X=\{2
Divisor_topology
relative effective Cartier divisor is roughly a family of effective Cartier divisors. Precisely, an effective Cartier divisor in a scheme X over a ring
Relative effective Cartier divisor
Relative_effective_Cartier_divisor
Standard division algorithm for multi-digit numbers
problems, one number, called the dividend, is divided by another, called the divisor, producing a result called the quotient. It enables computations involving
Long_division
Concept in algebraic geometry
V {\displaystyle V} , and any divisor in it may be called a canonical divisor. An anticanonical divisor is any divisor − K {\displaystyle K} with K {\displaystyle
Canonical_bundle
Algorithm for computing greatest common divisors
Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers, the largest number that divides them both without
Euclidean_algorithm
particularly ring theory, maximal common divisors are an abstraction of the number theory concept of greatest common divisor (GCD). This definition is slightly
Maximal_common_divisor
Integer having a non-trivial divisor
integers. Accordingly, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or
Composite_number
Graph of zero divisors of a commutative ring
combinatorial commutative algebra, a zero-divisor graph is an undirected graph representing the zero divisors of a commutative ring. It has elements of
Zero-divisor_graph
Method for computing the relation of two integers with their greatest common divisor
Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity,
Extended_Euclidean_algorithm
Mathematical result of division
general division). For example, when dividing 20 (the dividend) by 3 (the divisor), the quotient is 6 (with a remainder of 2) in the first sense and 6 +
Quotient
Type of Poulet number
every divisor d {\displaystyle d} divides 2 d − 2 {\displaystyle 2^{d}-2} . For example, 341 is a super-Poulet number: it has positive divisors (1, 11
Super-Poulet_number
Amount left over after computation
the operation that produces such a remainder when given a dividend and divisor. Alternatively, a remainder is also what is left after subtracting one
Remainder
Number equal to the sum of its proper divisors
the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2, and 3, and 1 + 2 + 3 =
Perfect_number
Class of natural numbers with many divisors
particular rigorous sense, has many divisors. Particularly, it is defined by a ratio between the number of divisors an integer has and that integer raised
Superior highly composite number
Superior_highly_composite_number
Singularities of algebraic varieties
union of coordinate hyperplanes. There are two variants of the concept, a divisor with normal crossings or with simple normal crossings. These can be considered
Normal_crossing_singularity
Mountain in Peru
Cono (literally: "Cone Hill") is a mountain located in the Sierra del Divisor National Park in the Ucayali Department of Peru. The mountain has never
Cerro_El_Cono
Integer which is the sum of its positive unitary divisors, not including itself
of its positive proper unitary divisors, not including the number itself. (A divisor d of a number n is a unitary divisor if d and n/d share no common factors
Unitary_perfect_number
(Mathematical) decomposition into a product
integer n, one needs an algorithm for finding a divisor q of n or deciding that n is prime. When such a divisor is found, the repeated application of this
Factorization
Number equal to the sum of all or some of its divisors
the sum of all or some of its proper divisors. A semiperfect number equal to the sum of all its proper divisors is a perfect number. The first few semiperfect
Semiperfect_number
useful identities related to number-theoretic divisor sums, i.e., sums of an arithmetic function over the divisors of a natural number n {\displaystyle n}
Divisor_sum_identities
Greatest common divisor of polynomials
In algebra, the greatest common divisor (frequently abbreviated GCD or gcd) of two polynomials is a polynomial, of the highest possible degree, which
Polynomial greatest common divisor
Polynomial_greatest_common_divisor
Two numbers without shared prime factors
relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides a does
Coprime_integers
special divisors is a result of William K. Clifford (1878) on algebraic curves, showing the constraints on special linear systems on a curve C. A divisor on
Clifford's theorem on special divisors
Clifford's_theorem_on_special_divisors
Positive integer that is the product of three distinct prime numbers
exactly eight divisors. If we express the sphenic number as n = p × q × r, where p, q, and r are distinct primes, then the set of divisors of n will be:
Sphenic_number
Computational operation
the Euclidean division of a by n, where a is the dividend and n is the divisor. For example, the expression "5 mod 2" evaluates to 1, because 5 divided
Modulo
Numbers with many divisors
a positive integer that has more divisors than all smaller positive integers. If d(n) denotes the number of divisors of a positive integer n, then a positive
Highly_composite_number
Shorthand way of determining whether a given number is divisible by a fixed divisor
useful way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits. Although
Divisibility_rule
Concept in algebraic geometry
In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear
Linear_system_of_divisors
Mountain range in South America
Sierra del Divisor is a mountain range located in the border between Peru and Brazil, rising up from the Amazonian plain. It is the only mountainous area
Sierra_del_Divisor
Species of fly
Laphria divisor is a species of robber flies in the family Asilidae. "Laphria divisor Report". Integrated Taxonomic Information System. Retrieved 2018-04-20
Laphria_divisor
National park in Acre, Brazil
The Serra do Divisor National Park (Portuguese: Parque Nacional da Serra do Divisor) is a 8,463 km2 (3,268 mi2) national park on the westernmost point
Serra do Divisor National Park
Serra_do_Divisor_National_Park
Species of marine polychaete
Myzostoma divisor is a species of parasitic marine polychaete in the order Myzostomida. M. divisor is a free-living, ectocommensal parasite of various
Myzostoma_divisor
On prime divisors in Fibonacci and Lucas sequences
positive discriminant, an element Un with n ≠ 1, 2, 6 has at least one prime divisor that does not divide any earlier one except the 12th Fibonacci number F(12) = U12(1
Carmichael's_theorem
Integers have unique prime factorizations
numbers. The canonical representations of the product, greatest common divisor (GCD), and least common multiple (LCM) of two numbers a and b can be expressed
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Method for allocating seats in parliaments
The D'Hondt method, also called the Jefferson method or the greatest divisors method, is an apportionment method for allocating seats in parliaments among
D'Hondt_method
Australian stock market index
price, not market capitalisation. Therefore, a fudge factor called the "Divisor" is used to ensure that the index value only changes when stock prices
S&P/ASX_200
Natural number
237,510 = harmonic divisor number 238,591 = number of free 13-ominoes 241,920 = highly totient number 242,060 = harmonic divisor number 248,832 = 125
100,000
Division with remainder of integers
(the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental
Euclidean_division
Algorithm for Euclidean division of polynomials
coefficient of the divisor, # because it is only used to normalize the dividend coefficients for j in range(1, len(divisor)): out[i + j] += -divisor[j] * coef
Synthetic_division
National park in Peru
Sierra del Divisor National Park (Spanish: Parque Nacional Sierra del Divisor) is a national park in the Amazon rainforest of Peru, established in 2015
Sierra del Divisor National Park
Sierra_del_Divisor_National_Park
Official world ranking for men's squash
previous 52 weeks is divided by the number of tournaments played (a minimum divisor of 11 is used) to give a ranking average. Where a player has played more
Men's_Squash_World_Rankings
Natural number
Cardinal one Ordinal 1st (first) Numeral system unary Factorization ∅ Divisors 1 Greek numeral Α´ Roman numeral I, i Greek prefix mono-/haplo- Latin prefix
1
Type of geometric transformation
the sense of category theory) way to turn a subvariety into a Cartier divisor. A blowup can also be called monoidal transformation, locally quadratic
Blowing_up
Commutative ring with a well behaved theory of prime factorization
(Weil) divisor. The Cartier divisors form a subgroup of the group of divisors containing the principal divisors. The quotient of the Cartier divisors by the
Krull_ring
Numbers obtained by adding the two previous ones
all odd prime divisors of Fn are congruent to 1 modulo 4, implying that all odd divisors of Fn (as the products of odd prime divisors) are congruent
Fibonacci_sequence
Natural number
has twelve divisors: 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. Thus, it is tied with number 693 for having the highest numbers of divisors for any odd
315_(number)
Number that is abundant but not semiperfect
of the proper divisors (divisors including 1 but not itself) of the number is greater than the number, but no subset of those divisors sums to the number
Weird_number
Natural number
divisible by the numbers from 1 to 4, and 6, a comparatively large number of divisors. It is central to many systems of timekeeping, including the Western calendar
12_(number)
Pair of integers related by their divisors
proper divisors of each is equal to the other number. That is, s(a)=b and s(b)=a, where s(n)=σ(n) − n is equal to the sum of positive divisors of n except
Amicable_numbers
Number whose sums of distinct divisors represent all smaller numbers
divisors of n {\displaystyle n} . For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors
Practical_number
Number with a half-integer abundancy index
k/2 for an odd integer k, where σ(n) is the sum-of-divisors function, the sum of all positive divisors of n. The first few hemiperfect numbers are: 2, 24
Hemiperfect_number
On prime divisors of differences two nth powers
{\displaystyle n\geq 1} , there is a prime number p (called a primitive prime divisor) that divides a n − b n {\displaystyle a^{n}-b^{n}} and does not divide
Zsigmondy's_theorem
Method for division with remainder
{\displaystyle N/D=(Q,R)} , where N = numerator (dividend) D = denominator (divisor) is the input, and Q = quotient R = remainder is the output. The simplest
Division_algorithm
Irreducible polynomial whose roots are nth roots of unity
polynomial with integer coefficients that is a divisor of x n − 1 {\displaystyle x^{n}-1} and is not a divisor of x k − 1 {\displaystyle x^{k}-1} for any
Cyclotomic_polynomial
Base-dependent property of integers
b^{p}} do Kaprekar numbers and cycles exist. If d {\displaystyle d} is any divisor of p {\displaystyle p} , then n {\displaystyle n} is also a p {\displaystyle
Kaprekar_number
Fully simplified fraction
which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). In other words,
Irreducible_fraction
Every subgroup of a cyclic group is cyclic, and if finite, its order divides its parent's
group of order n, every subgroup's order is a divisor of n, and there is exactly one subgroup for each divisor. This result has been called the fundamental
Subgroups_of_cyclic_groups
Natural number
A054979 (e-perfect numbers: numbers k such that the sum of the e-divisors (exponential divisors) of k equals 2*k.)". The On-Line Encyclopedia of Integer Sequences
1980_(number)
Abundant number whose proper divisors are all deficient numbers
whose proper divisors are all deficient numbers. For example, 20 is a primitive abundant number because: The sum of its proper divisors is 1 + 2 + 4 +
Primitive_abundant_number
Complex number whose real and imaginary parts are both integers
common divisor (gcd) of two Gaussian integers a, b is a Gaussian integer d that is a common divisor of a and b, which has all common divisors of a and
Gaussian_integer
Numbers whose sum of divisors is twice the number minus 1
such that the sum of all divisors of n (the sum-of-divisors function σ(n)) is equal to 2n − 1, the sum of all proper divisors of n, s(n) = σ(n) − n, then
Almost_perfect_number
Number whose divisors add to a multiple of that number
called k-perfect (or k-fold perfect) if the sum of all positive divisors of n (the divisor function, σ(n)) is equal to kn; a number is thus perfect if and
Multiply_perfect_number
Number without repeated prime factors
m {\displaystyle m} is the largest divisor of n {\displaystyle n} such that m 2 {\displaystyle m^{2}} is a divisor of n {\displaystyle n} . Every positive
Square-free_integer
Concept in algebraic geometry
between line bundles and divisors (built from codimension-1 subvarieties), there is an equivalent notion of an ample divisor. In more detail, a line bundle
Ample_line_bundle
Class of apportionment methods
rank-index methods are a set of apportionment methods that generalize the divisor method. These have also been called Huntington methods, since they generalize
Rank-index_method
Decomposition of a number into a product
order dividing 2 to obtain a coprime factorization of the largest odd divisor of Δ in which Δ = −4ac or Δ = a(a − 4c) or Δ = (b − 2a)(b + 2a). If the
Integer_factorization
Type of figurate number
h_{n}} divisors. Proof. r n − 1 = ( p 2 q ) n − 1 = p 2 ( n − 1 ) q n − 1 {\displaystyle r^{n-1}=(p^{2}q)^{n-1}=p^{2(n-1)}q^{n-1}} has divisors of the
Hexagonal_number
Way to break a division problem into smaller steps
mental arithmetic, which could limit the size of the divisor. For most people, small integer divisors up to 12 are handled using memorised multiplication
Short_division
Numbers whose sum of divisors is twice the number plus 1
quasiperfect number is a natural number n for which the sum of all its divisors (the sum-of-divisors function σ ( n ) {\displaystyle \sigma (n)} ) is equal to 2
Quasiperfect_number
Concept in algebraic geometry
correspondence between line bundles and divisors (built from codimension-1 subvarieties), there is an equivalent notion of a nef divisor. More generally, a line bundle
Nef_line_bundle
Declarative, general-purpose programming language
common divisor (GCD) of two numbers. It is intended to demonstrate the declarative nature of Gödel, not to be particularly efficient. The CommonDivisor predicate
Gödel_(programming_language)
Singularities of algebraic varieties
f\colon Y\to X} be a resolution of singularities of X. Using that Cartier divisors can be pulled back, one can write K Y = f ∗ ( K X ) + ∑ i a i E i {\displaystyle
Canonical_singularity
Number that cannot be written as an aliquot sum
positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer. That is, these numbers are not in the image of
Untouchable_number
Mathematical principles
some real number }}H\}.} Divisor methods differ by the method they use for rounding. A divisor method is parametrized by a divisor function d ( k ) {\displaystyle
Mathematics_of_apportionment
Australian stock market index
of the divisor. The divisor can be calculated: D i v i s o r = M V I n d e x V a l u e {\displaystyle Divisor={MV \over
S&P/ASX_300
DIVISOR
DIVISOR
DIVISOR
DIVISOR
Boy/Male
Tamil
King, Shantanus father
Boy/Male
French
Works in iron.
Boy/Male
Muslim
Judge
Boy/Male
Australian, French, Irish
Silent
Boy/Male
Latin
Strong and healthy.
Boy/Male
Indian, Punjabi, Sikh
Great Elixir
Boy/Male
British, English
Brewer
Girl/Female
Muslim
Transmitter of ancient Arabic poetry
Girl/Female
Latin
Dark.
Girl/Female
Arabic, Muslim
Laaibah is the Prettiest Women in All the Jannats (Heavens)
DIVISOR
DIVISOR
DIVISOR
DIVISOR
DIVISOR
n.
The operation of striking out common factors, in both the dividend and divisor.
n.
The number by which the dividend is divided.