30 (thirty) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
29 and preceding
31.
In mathematics

30 is an
even,
composite
Composite or compositing may refer to:
Materials
* Composite material, a material that is made from several different substances
** Metal matrix composite, composed of metal and other parts
** Cermet, a composite of ceramic and metallic material ...
, and
pronic number
A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n(n+1).. The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers,. or rectangular number ...
. With
2,
3, and
5 as its
prime factor
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
s, it is a
regular number
Regular numbers are numbers 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, 602 = 3600 = 48 ×&nb ...
and the first
sphenic number
In number theory, a sphenic number (from , 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definition
A sphenic ...
, the smallest of the form , where is a prime greater than 3. It has an
aliquot sum
In number theory, the aliquot sum of a positive integer is the sum of all proper divisors of , that is, all divisors of other than itself.
That is,
s(n)=\sum_ d \, .
It can be used to characterize the prime numbers, perfect numbers, sociabl ...
of
42; within an
aliquot sequence
In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0.
Def ...
of thirteen composite numbers (30,
42,
54,
66,
78,
90,
144 144 may refer to:
* 144 (number), the natural number following 143 and preceding 145
* AD 144, a year of the Julian calendar, in the second century AD
* 144 BC, a year of the pre-Julian Roman calendar
* 144 (film), ''144'' (film), a 2015 Indian com ...
,
259
Year 259 ( CCLIX) was a common year starting on Saturday of the Julian calendar. At the time, it was known as the Year of the Consulship of Aemilianus and Bassus (or, less frequently, year 1012 ''Ab urbe condita''). The denomination 259 for thi ...
,
45,
33,
15,
9,
4,
3,
1, 0) to the Prime in the
3-aliquot tree. From
1 to the number 30, this is the longest Aliquot Sequence.
It is also:
* A
semiperfect number
In number theory, a semiperfect number or pseudoperfect number is a natural number ''n'' that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number. ...
, since adding some subsets of its divisors (e.g., 5, 10 and 15) equals 30.
* A
primorial
In mathematics, and more particularly in number theory, primorial, denoted by "", is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, the function ...
.
* A
Harshad number
In mathematics, a harshad number (or Niven number) in a given radix, number base is an integer that is divisible by the digit sum, sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers ...
in
decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of th ...
.
* Divisible by the number of
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
s (
10) below it.
* The largest number such that all
coprime
In number theory, two integers and are coprime, 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 does not divide , and vice versa. This is equiv ...
s smaller than itself, except for 1, are prime.
* The sum of the first four squares, making it a
square pyramidal number
In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid (geometry), pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part ...
.
* The number of
vertices in the
Tutte–Coxeter graph
In the mathematics, mathematical field of graph theory, the Tutte–Coxeter graph or Tutte eight-cage or Cremona–Richmond graph is a 3-regular graph with 30 vertices and 45 edges. As the unique smallest cubic graph of girth (graph theory), girt ...
.
* The measure of the
central angle
A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arc l ...
and
exterior angle
In geometry, an angle of a polygon is formed by two adjacent sides. For a simple polygon (non-self-intersecting), regardless of whether it is convex or non-convex, this angle is called an internal angle (or interior angle) if a point withi ...
of a
dodecagon
In geometry, a dodecagon, or 12-gon, is any twelve-sided polygon.
Regular dodecagon
A regular polygon, regular dodecagon is a figure with sides of the same length and internal angles of the same size. It has twelve lines of reflective symmetry ...
, which is the
petrie polygon
In geometry, a Petrie polygon for a regular polytope of dimensions is a skew polygon in which every consecutive sides (but no ) belongs to one of the facets. The Petrie polygon of a regular polygon is the regular polygon itself; that of a reg ...
of the
24-cell
In four-dimensional space, four-dimensional geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is also called C24, or the icositetrachoron, octaplex (short for "octa ...
.
* The number of
sides of a
triacontagon
In geometry, a triacontagon or 30-gon is a thirty-sided polygon. The sum of any triacontagon's interior angles is 5040 (number), 5040 degrees.
Regular triacontagon
The ''regular polygon, regular triacontagon'' is a constructible polygon, by an ...
, which in turn is the petrie polygon of the
120-cell
In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol . It is also called a C120, dodecaplex (short for "dodecahedral complex"), hyperdodecahedron, polydodecahedron, hec ...
and
600-cell
In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol .
It is also known as the C600, hexacosichoron and hexacosihedroid.
It is also called a tetraplex (abbreviated from ...
.
* The number of edges of a
dodecahedron
In geometry, a dodecahedron (; ) or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three Kepler–Po ...
and
icosahedron
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes . The plural can be either "icosahedra" () or "icosahedrons".
There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrical tha ...
, of vertices of an
icosidodecahedron
In geometry, an icosidodecahedron or pentagonal gyrobirotunda is a polyhedron with twenty (''icosi-'') triangular faces and twelve (''dodeca-'') pentagonal faces. An icosidodecahedron has 30 identical Vertex (geometry), vertices, with two triang ...
, and of
faces
The face is the front of the head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may affect the ...
of a
rhombic triacontahedron
The rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombus, rhombic face (geometry), faces. It has 60 edge (geometry), edges and 32 vertex ...
.
* The sum of the number of
elements of a
5-cell
In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol . It is a 5-vertex four-dimensional space, four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, hypertetrahedron, pentachoron, pentatope, pe ...
: 5 vertices, 10
edges, 10
faces
The face is the front of the head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may affect the ...
, and 5
cells
Cell most often refers to:
* Cell (biology), the functional basic unit of life
* Cellphone, a phone connected to a cellular network
* Clandestine cell, a penetration-resistant form of a secret or outlawed organization
* Electrochemical cell, a d ...
.
* The
Coxeter number
In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections. The product depends on the order in which they are taken, but different orderings produce conjugate elements, which ha ...
of
''E''8.
* A
largely composite number
A highly composite number is 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 integer ''N'' is highly composite if ''d''(' ...
,
as it has 8
divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a '' multiple'' of m. An integer n is divisible or evenly divisibl ...
s and no smaller number has more than 8 divisors
Furthermore,
In a
group
A group is a number of persons or things that are located, gathered, or classed together.
Groups of people
* Cultural group, a group whose members share the same cultural identity
* Ethnic group, a group whose members share the same ethnic iden ...
, such that
, where does not divide , and has a subgroup of order
, 30 is the only number less than 60 that is neither a prime nor of the aforementioned form. Therefore, 30 is the only candidate for the order of a
simple group
SIMPLE Group Limited is a conglomeration of separately run companies that each has its core area in International Consulting. The core business areas are Legal Services, Fiduciary Activities, Banking Intermediation and Corporate Service.
The d ...
less than 60, in which one needs other methods to specifically reject to eventually deduce said order.
The
SI prefix
The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official st ...
for 10
30 is
Quetta- (Q), and for 10
−30 (i.e., the reciprocal of 10
30)
quecto
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pre ...
(q). These numbers are the largest and smallest number to receive an SI prefix to date.
In other fields
Thirty is:
* Used (as
–30–
-30- has been traditionally used by journalists in North America to indicate the end of a story or article that is submitted for editing and typesetting. It is commonly employed when writing on deadline and sending bits of the story at a time, v ...
) to indicate the end of a newspaper (or broadcast) story, a copy editor's typographical notation
* The number of days in the months April, June, September and November (and in unusual circumstances February—see
February 30
Several non-standard dates are used in calendars for various purposes: some are expressly fictional, some are intended to produce a rhetorical effect (such as sarcasm), and others attempt to address a particular mathematical, scientific or acc ...
). Although the number of days in a month vary, 30 is used to estimate months elapsing.
* In years of marriage, the pearl
wedding anniversary
A wedding anniversary is the anniversary of the date that a wedding took place. Couples often mark the occasion by celebrating their relationship, either privately or with a larger party. Special celebrations and gifts are often given for partic ...
* The international calling code for
Greece
Greece, officially the Hellenic Republic, is a country in Southeast Europe. Located on the southern tip of the Balkan peninsula, it shares land borders with Albania to the northwest, North Macedonia and Bulgaria to the north, and Turkey to th ...
History and literature
* Age 30 is when Jewish priests traditionally start their service (according to Numbers 4:3).
* One of the rallying cries of the 1960s student/youth protest movement was the slogan, "
Don't trust anyone over thirty".
* In ''
The Myth of Sisyphus
''The Myth of Sisyphus'' () is a 1942 Philosophy, philosophical work by Albert Camus. Influenced by philosophers such as Søren Kierkegaard, Arthur Schopenhauer, and Friedrich Nietzsche, Camus introduces his philosophy of the absurdism, absurd. T ...
'' the French existentialist
Albert Camus
Albert Camus ( ; ; 7 November 1913 – 4 January 1960) was a French philosopher, author, dramatist, journalist, world federalist, and political activist. He was the recipient of the 1957 Nobel Prize in Literature at the age of 44, the s ...
comments that the age of thirty is a crucial period in the life of a man, for at that age he gains a new awareness of the meaning of time.
References
{{DEFAULTSORT:30 (Number)
Integers