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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
Integer that divides another integer
non-trivial divisors. There are divisibility rules that allow one to recognize certain divisors of a number from the number's digits. 7 is a divisor of 42 because
Divisor
Mathematical table
is a composition of sequences OEIS: A103431 and OEIS: A103432. Norm 1–250 251–500 501–750 751–1000 Gaussian integer Table of divisors Integer factorization
Table of Gaussian integer factorizations
Table_of_Gaussian_integer_factorizations
Arithmetic function related to the divisors of an integer
divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors
Divisor_function
and then multiplying them. Divisors and properties related to divisors are shown in table of divisors. Fundamental theorem of arithmetic – Integers have
Table_of_prime_factors
Numbers with many divisors
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
American stock market index composed of 30 industry leaders
following table shows the annual returns of the DJIA since 1896: The DJIA is computed as the sum of the prices of all thirty stocks divided by a divisor, the
Dow_Jones_Industrial_Average
Table of derivatives Table of divisors Table of integrals Table of mathematical symbols Table of prime factors Taylor series Timeline of mathematics Trigonometric
List of mathematics reference tables
List_of_mathematics_reference_tables
Integer having a non-trivial divisor
three divisors. In the case of squares of primes, those divisors are { 1 , p , p 2 } {\displaystyle \{1,p,p^{2}\}} . A number n that has more divisors than
Composite_number
lemma Extended Euclidean algorithm Table of divisors Prime number, prime power Bonse's inequality Prime factor Table of prime factors Formula for primes
List_of_number_theory_topics
Number divisible only by 1 and itself
the numbers with exactly two positive divisors. Those two are 1 and the number itself. As 1 has only one divisor, itself, it is not prime by this definition
Prime_number
tolerancing Well-known text representation of geometry List of logic symbols List of mathematical constants Table of mathematical symbols by introduction date
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Blue chip stock market index
across all index components. The index divisors, which is adjusted to maintain the continuity of the values of the index across changes due to corporate
EURO_STOXX_50
Number whose sums of distinct divisors represent all smaller numbers
numbers from 1 to 11 can be expressed as sums of its divisors 1, 2, 3, 4, and 6: as well as these divisors themselves, we have 5 = 3 + 2, 7 = 6 + 1, 8 = 6
Practical_number
Natural number
because some of its proper divisors; 1, 2, 3, and 6; sum to 12. 12 is a highly composite number because it has 6 divisors, more than any number less than
12_(number)
Number with a half-integer abundancy index
of the divisors of 24 is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60 = 5/2 × 24. The abundancy index is 5/2 which is a half-integer. The following table gives
Hemiperfect_number
Hypercomplex number system
Cayley–Dickson construction also contain zero divisors. The sedenion multiplication table is shown below: From the above table, we can see that: e 0 e i = e i e 0
Sedenion
This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no divisors other than 1 and itself
List_of_prime_numbers
Natural number
as a sum of some of its divisors, making it a semiperfect number. The geometric mean of its nine divisors is 10. 100 is the sum of the cubes of the first
100
Error-detecting code for detecting data changes
will result in a certain proportion of missed errors, due to the quotient ring having zero divisors. The advantage of choosing a primitive polynomial as
Cyclic_redundancy_check
Rule for proportional allocation
Hayes. The two names for these methods—highest averages and divisors—reflect two different ways of thinking about them, and their two independent inventions
Highest_averages_method
Hypercomplex number system
contain zero divisors and are thus not a division algebra. Whereas the sedenions have 84 zero divisors, the trigintaduonions have 1,260 zero divisors derived
Trigintaduonion
Natural number
is a perfect cube. Sphenic numbers always have exactly eight divisors. 8 is the base of the octal number system. A polygon with eight sides is an octagon
8
Natural number
because the sum of its proper divisors (66), is greater than itself. Like all multiples of 6, 54 is equal to some of its proper divisors summed together
54_(number)
Natural number
thirteenth prime number and sixth super-prime. Its arithmetic mean of its six divisors is twenty-eight, where (6, 28) represent the first two perfect numbers
92_(number)
Natural number
smallest number with exactly 11 divisors (but there are smaller numbers with more than 11 divisors; e.g., 60 has 12 divisors) (sequence A005179 in the OEIS)
1024_(number)
Topics referred to by the same term
information Digital content, content that exists in the form of digital data Table of contents, a list of chapters or sections in a document Content (Centreville
Content
On prime divisors in Fibonacci and Lucas sequences
F(2) = 1, which have no prime divisors F(6) = 8, whose only prime divisor is 2 (which is F(3)) F(12) = 144, whose only prime divisors are 2 (which is F(3)) and
Carmichael's_theorem
Way to break a division problem into smaller steps
sometimes at the expense of relying on mental arithmetic, which could limit the size of the divisor. For most people, small integer divisors up to 12 are handled
Short_division
their positive proper divisors, which are divisors excluding the number itself. So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3
List of Mersenne primes and perfect numbers
List_of_Mersenne_primes_and_perfect_numbers
Natural number
number of 1. Group 1 of the periodic table consists of hydrogen and the alkali metals. In philosophy, the number 1 is commonly regarded as a symbol of unity
1
Natural number
19 {\displaystyle 3\cdot 19} , and is therefore a semiprime. Its proper divisors are 1, 3, and 19, whose sum is 23, so 57 is a deficient number. Since both
57_(number)
Number whose divisors add to a multiple of that number
generalization of a perfect number. For a given natural number k, a number n is called k-perfect (or k-fold perfect) if the sum of all positive divisors of n (the
Multiply_perfect_number
Arithmetic operation
dividend, which is divided by the divisor, and the result is called the quotient. At an elementary level the division of two natural numbers is, among other
Division_(mathematics)
Two-dimensional group theory table
prime divisors of the orders of the elements of each conjugacy class of a finite group can be deduced from its character table (an observation of Graham
Character_table
to sums of an arithmetic function over just the proper prime divisors of n {\displaystyle n} . We also define periodic variants of these divisor sums with
Divisor_sum_identities
Numbers whose aliquot sums form a cyclic sequence
of order 1, or a perfect number—for example, the proper divisors of 6 are 1, 2, and 3, whose sum is again 6. A pair of amicable numbers is a set of sociable
Sociable_number
Number without repeated prime factors
first step of all standard factorization algorithms. The square-free part of n {\displaystyle n} is the product of all prime divisors of n {\displaystyle
Square-free_integer
Two or more natural numbers with a common abundancy index
_{k}} denotes a divisor function with σ k ( n ) {\displaystyle \sigma _{k}(n)} equal to the sum of the k-th powers of the divisors of n. The numbers 1
Friendly_number
Online database of integer sequences
MATHEMATICA muDD[d_] := MoebiusMu[d]*d^2; Table[Plus @@ muDD[Divisors[n]], {n, 60}] (Lopez) Flatten[Table[{ x = FactorInteger[n]; p = 1; For[i = 1, i
On-Line Encyclopedia of Integer Sequences
On-Line_Encyclopedia_of_Integer_Sequences
Multi-winner electoral system
party divisor is initialized with 1. Effectively, the objective of the iterative process is to modify the regional divisors and party divisors so that
Biproportional_apportionment
Shorthand way of determining whether a given number is divisible by a fixed divisor
in the divisor. For instance, one cannot make a rule for 14 that involves multiplying the equation by 7. This is not an issue for prime divisors because
Divisibility_rule
Standard division algorithm for multi-digit numbers
divisors which have a finite or terminating decimal expansion (i.e. decimal fractions). In this case the procedure involves multiplying the divisor and
Long_division
Number whose square is a given number
zero divisor. Thus in rings where zero divisors do not exist, it is uniquely 0. However, rings with zero divisors may have multiple square roots of 0. For
Square_root
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
Number in {..., –2, –1, 0, 1, 2, ...}
integers map to zero in certain rings. The lack of zero divisors in the integers (last property in the table) means that the commutative ring Z {\displaystyle
Integer
Function whose domain is the positive integers
of both classes. An example of an arithmetic function is the divisor function whose value at a positive integer n is equal to the number of divisors of
Arithmetic_function
Philosophical system based on the teachings of Pythagoras
numbers as those that were equal to the sum of all their divisors. For example: 28 = 1 + 2 + 4 + 7 + 14. The theory of odd and even numbers was central to Pythagorean
Pythagoreanism
Four-dimensional number system
real numbers. The next extension gives the sedenions, which have zero divisors and so cannot be a normed division algebra. The unit quaternions give a
Quaternion
Algorithm for computing greatest common divisors
there are two versions of the Euclidean algorithm, one for right divisors and one for left divisors. Choosing the right divisors, the first step in finding
Euclidean_algorithm
Numbers that evenly divide powers of 60
that evenly divide powers of 60 (or, equivalently, powers of 30). Equivalently, they are the numbers whose only prime divisors are 2, 3, and 5. As an example
Regular_number
Number-theoretical function
number of divisors of n {\displaystyle n} which are congruent to 1 modulo 4 and d 3 ( n ) {\displaystyle d_{3}(n)} is the number of divisors of n {\displaystyle
Sum_of_squares_function
7560 A perfect number is an integer that is the sum of its positive proper divisors (all divisors except itself). The first 10 perfect numbers: 6
List_of_numbers
Mapping arbitrary data to fixed-size values
by selecting a divisor M which is a prime number close to the table size, so h(K) ≡ K (mod M). The table size is usually a power of 2. This gives a distribution
Hash_function
Mathematical recursive sequence
the only proper divisor of a prime is 1), followed by 0 (since 1 has no proper divisors). See (sequence A080907 in the OEIS) for a list of such numbers up
Aliquot_sequence
Bug in the Intel P5 Pentium floating-point unit
bad divisors the running time would double since each FDIV would take about 80 clock cycles instead of the usual 40 cycles. With more random divisors the
Pentium_FDIV_bug
Computational operation
language and the signs of a or n. Standard Pascal and ALGOL 68, for example, give a positive remainder (or 0) even for negative divisors, and some programming
Modulo
Last letter of the Greek alphabet
space, or total set of possible outcomes. In triangle geometry, Brocard points. In number theory, Ω(n) is the number of prime divisors of n (counting multiplicity)
Omega
German state election
increasing the total number of seats. The seat distribution for state and district lists uses the Sainte-Laguë/Schepers divisor method with standard rounding
2026 Rhineland-Palatinate state election
2026_Rhineland-Palatinate_state_election
Mathematical function, inverse of an exponential function
logarithm tables, tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition. This is possible because the logarithm of a
Logarithm
Base sixty numeral system
superior highly composite number, has twelve divisors, namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers. With
Sexagesimal
Finite sum of distinct unit fractions
sum of divisors of the denominator; this is possible whenever the denominator is a practical number, and Liber Abaci includes tables of expansions of this
Egyptian_fraction
Method for computing the relation of two integers with their greatest common divisor
computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity, which are integers x and y
Extended_Euclidean_algorithm
Mathematical concept
the j-invariant of the smooth fibers. (Thus MS is a Q-linear equivalence class of Q-divisors, using the identification between the divisor class group Cl(S)
Elliptic_surface
using a divisor of 1.4 instead of 1, is used to allocate both the constituency and leveling seats. A party must cross the electoral threshold of 4% of the
2029 Norwegian parliamentary election
2029_Norwegian_parliamentary_election
Family of voting systems
= 2, B = 2, C = 1 Same as Sainte-Laguë but first divisor is 1.4 to favour larger parties. Divisors: 1.4, 3, 5, ... Result: A = 2, B = 2, C = 1 The Hare
Party-list proportional representation
Party-list_proportional_representation
calculation, a divisor is chosen by the Federal Returning Officer so that the total number of seats to be allocated are distributed. The tables below reflect
Results of the 2025 German federal election
Results_of_the_2025_German_federal_election
Mass balance consistency check for a chemical reaction
An ICE table or RICE box or RICE chart is a tabular system of keeping track of changing concentrations in an equilibrium reaction. This includes vaporization
RICE_chart
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
Doubly exponential integer sequence
technique he found that 1166 out of the first three million primes are divisors of Sylvester numbers, and that none of these primes has a square that divides
Sylvester's_sequence
Base-12 numeral system
number of denominators that give terminating fractions within a given number of digits, n, in a base b is the number of factors (divisors) of b n {\displaystyle
Duodecimal
Search (GIMPS). A prime number is a natural number greater than 1 with no divisors other than 1 and itself. Euclid's theorem proves that for any given prime
Largest_known_prime_number
Official world ranking for men's squash
as shown in the table below (the minimum divisor is eleven). The average is calculated from the highest points scored for this number of events over the
Men's_Squash_World_Rankings
Geometrical GCD and LCM algorithm
the greatest common divisor (GCD) of two natural numbers. It makes use of reflections inside a rectangle that has sides with length of the two given numbers
Arithmetic_billiards
Mathematical treatise by Euclid
algorithm for greatest common divisors, Euclid's theorem that there are infinitely many prime numbers, and the construction of regular polygons and polyhedra
Euclid's_Elements
Natural number
1-automorphic number 1,808,141,741 : number of partitions of 280 into divisors of 280 1,808,676,326 : number of 38-bead necklaces (turning over is allowed)
1,000,000,000
Branch of pure mathematics
is the probability that it will have many more or many fewer divisors or prime divisors than the average? Combinatorics in number theory starts with questions
Number_theory
Problem-solving technique and algorithmic paradigm
algorithm that finds the divisors of a natural number n would enumerate all integers from 1 to n, and check whether each of them divides n without remainder
Brute-force_search
Natural number
a^{n}-b^{n}=1} having no prime divisors, n = 2 {\displaystyle n=2} , a + b {\displaystyle a+b\;} a power of two, where any odd prime factors of a 2 − b 2 = ( a + b
63_(number)
Type of natural number
n=1+k(\sigma (n)-n-1)} holds, where σ(n) is the divisor function (i.e., the sum of all positive divisors of n). A hyperperfect number is a k-hyperperfect
Hyperperfect_number
Algorithm for Euclidean division of polynomials
algorithm; this algorithm includes steps for dividing non-monic divisors: Write the coefficients of the dividend on a bar. a 7 a 6 a 5 a 4 a 3 a 2 a 1 a 0
Synthetic_division
Decomposition of a number into a product
b, c) that is an element f ∈ GΔ of order dividing 2 to obtain a coprime factorization of the largest odd divisor of Δ in which Δ = −4ac or Δ = a(a −
Integer_factorization
Concept in mathematical group theory
prime divisors of the orders of the elements of each conjugacy class of a finite group can be deduced from its character table (an observation of Graham
Character_theory
divisors Exponentiation (power) – Repeated multiplication Square root – Reversal of a power of 2 (exponent of 1/2) Cube root – Reversal of a power of
Outline_of_arithmetic
(Mathematical) decomposition into a product
domains (UFD). Greatest common divisors exist in UFDs, but not every integral domain in which greatest common divisors exist (known as a GCD domain) is
Factorization
Mathematical constant
4007/annals.2008.168.367. MR 2434882. Koukoulopoulos, Dimitris (2010). "Divisors of shifted primes". International Mathematics Research Notices. 2010 (24):
Erdős–Tenenbaum–Ford_constant
Victorian tables were used in Gaul (now France) and Spain until they were displaced by Dionysian tables at the end of the 8th century. The tables of Dionysius
Date_of_Easter
Function studied by Ramanujan
{N} } , the divisor function σ k ( n ) {\displaystyle \sigma _{k}(n)} is the sum of the k {\displaystyle k} th powers of the divisors of n {\displaystyle
Ramanujan_tau_function
Logical connective
operator, build the Boolean algebra of propositional logic. Example of a 4-element Boolean algebra: the 4 divisors {1,2,3,6} of 6 with 1 as zero and 6 as unity
Converse_nonimplication
Natural number
sum of any number's proper divisors. 304 is a nontotient number because it is an even number and phi(x) = 304 has no solution. It is the sum of consecutive
300_(number)
Mathematical table
mathematical work, includes a mathematical table for converting rational numbers of the form 2/n into Egyptian fractions (sums of distinct unit fractions), the form
Rhind Mathematical Papyrus 2/n table
Rhind_Mathematical_Papyrus_2/n_table
Integer factorization algorithm
for numbers up to 655372 = 4,295,098,369. Preparing such a table (usually via the Sieve of Eratosthenes) would only be worthwhile if many numbers were
Trial_division
Algebra over a field with only invertible elements and zero
zero divisors. A finite-dimensional unital associative algebra (over any field) is a division algebra if and only if it has no nonzero zero divisors. Indeed
Division_algebra
Country in South America
the Earth on the Earth's surface because of the ellipsoid shape of the planet. The Andes is the watershed divisor between the Amazon watershed, which runs
Ecuador
Algebraic manipulation of "true" and "false"
the positive divisors of n. Hence those divisors form a Boolean algebra. These divisors are not subsets of a set, making the divisors of n a Boolean algebra
Boolean_algebra
the sequence is bounded? Gillies' conjecture on the distribution of prime divisors of Mersenne numbers. Landau's problems Goldbach conjecture: all even
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Whole number
instead of a dot with overline. The earliest use of zero in the calculation of the Julian Easter occurred before AD 311, at the first entry in a table of epacts
0
Number used for counting
× c). No nonzero zero divisors: if a and b are natural numbers such that a × b = 0, then a = 0 or b = 0 (or both). For most of history, what are now called
Natural_number
Cardinality of a mathematical group, or of the subgroup generated by an element
the order |a| of any element is a divisor of |G|. The symmetric group S3 has the following multiplication table. This group has six elements, so ord(S3) =
Order_(group_theory)
Ancient Greek mathematician (fl. 300 BC)
includes the Euclidean algorithm, a method for finding the greatest common divisor of two numbers. The 8th book discusses geometric progressions, while book
Euclid
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TABLE OF-DIVISORS
TABLE OF-DIVISORS
TABLE OF-DIVISORS
TABLE OF-DIVISORS
TABLE OF-DIVISORS
TABLE OF-DIVISORS
TABLE OF-DIVISORS
TABLE OF-DIVISORS
TABLE OF-DIVISORS
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