360 (three hundred ndsixty) 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 359 and preceding 361.

In mathematics

* 360 is the 13th

highly 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''(' ...

and one of only seven numbers such that no number less than twice as much has more divisors; the others are 1, 2, 6, 12, 60, and 2520 . *360 is also the 6th

superior highly composite number In number theory, a superior highly composite number is a natural number which, in a 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 to s ...

, the 6th colossally abundant number, a refactorable number, a 5-

smooth number In number theory, an ''n''-smooth (or ''n''-friable) number is an integer whose prime factors are all less than or equal to ''n''. For example, a 7-smooth number is a number in which every prime factor is at most 7. Therefore, 49 = 72 and 15750 = 2 ...

, and a Harshad number 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 ...

since the sum of its digits ( 9) is a divisor of 360. *360 is divisible by the number of its divisors ( 24), and it is the smallest number divisible by every natural number from 1 to 10, except 7. Furthermore, one of the divisors of 360 is 72, which is the number of primes below it. *360 is the sum of

twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...

s ( 179 + 181) and the sum of four consecutive powers of three (9 + 27 + 81 + 243). *The sum of

Euler's totient function In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In ot ...

φ(x) over the first thirty-four

integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

s is 360. *360 is a triangular matchstick number. *360 is the product of the first two

unitary perfect number A unitary perfect number is an integer which is the sum 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). The numb ...

60 \times 6 = 360.

*There are 360 even permutations of 6 elements. They form the

alternating group In mathematics, an alternating group is the Group (mathematics), group of even permutations of a finite set. The alternating group on a set of elements is called the alternating group of degree , or the alternating group on letters and denoted ...

A₆. A turn is divided into 360 degrees for

angular measurement In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight lines at a point. Formally, an angle is a figure lying in a plane formed by two rays, called the '' sides'' of the angle, sharing ...

. is also called a round angle. This unit choice divides round angles into equal

sectors Sector may refer to: Places * Sector, West Virginia, U.S. Geometry * Circular sector, the portion of a disc enclosed by two radii and a circular arc * Hyperbolic sector, a region enclosed by two radii and a hyperbolic arc * Spherical sector, a ...

measured in integer rather than fractional degrees. Many angles commonly appearing in

planimetrics Planimetrics is the study of plane measurements, including angles, distances, and areas. History To measure planimetrics a planimeter or dot planimeter is used. This rather advanced analog technology is being taken over by simple image measu ...

have an integer number of degrees. For a

simple Simple or SIMPLE may refer to: *Simplicity, the state or quality of being simple Arts and entertainment * ''Simple'' (album), by Andy Yorke, 2008, and its title track * "Simple" (Florida Georgia Line song), 2018 * "Simple", a song by John ...

non-intersecting

polygon In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...

, the sum of the

internal angle In geometry, an angle of a polygon is formed by two adjacent edge (geometry), sides. For a simple polygon (non-self-intersecting), regardless of whether it is Polygon#Convexity and non-convexity, convex or non-convex, this angle is called an ...

s of a

quadrilateral In Euclidean geometry, geometry a quadrilateral is a four-sided polygon, having four Edge (geometry), edges (sides) and four Vertex (geometry), corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''l ...

always equals 360 degrees.

Integers from 361 to 369

361

361=19^2,

centered triangular number,

centered octagonal number A centered octagonal number is a centered number, centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are th ...

, centered decagonal number, member of the Mian–Chowla sequence. There are also 361 positions on a standard 19 × 19 Go board.

362

362=2\times181=\sigma_2(19)

: sum of squares of divisors of 19, Mertens function returns 0, nontotient, noncototient.

363

364

364=2^2\times 7\times 13

tetrahedral number A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid (geometry), pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular ...

, sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0,

nontotient In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotie ...

. It is a

repdigit In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of "repeated" and "digit". Ex ...

in bases three (111111),

nine 9 (nine) is the natural number following and preceding . Evolution of the Hindu–Arabic digit Circa 300 BC, as part of the Brahmi numerals, various Indians wrote a digit 9 similar in shape to the modern closing question mark without the bot ...

(444), twenty-five (EE), twenty-seven (DD), fifty-one (77), and ninety (44); the sum of six consecutive powers of three (1 + 3 + 9 + 27 + 81 + 243); and the twelfth non-zero

365

365 is the amount of days in a common year. For the common year, see

common year A common year is a calendar year with 365 days, as distinguished from a ''leap year'', which has 366 days. More generally, a common year is one without Intercalation (timekeeping), intercalation. The Gregorian calendar, used by the majority of ...

366

366=2\times 3\times 61,

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 ...

, Mertens function returns 0, noncototient, number of complete partitions of 20, 26-gonal and 123-gonal. There are also 366 days in a

leap year A leap year (also known as an intercalary year or bissextile year) is a calendar year that contains an additional day (or, in the case of a lunisolar calendar, a month) compared to a common year. The 366th day (or 13th month) is added to keep t ...

367

367 is a prime number,

Perrin number In mathematics, the Perrin numbers are a doubly infinite constant-recursive sequence, constant-recursive integer sequence with Characteristic equation (calculus), characteristic equation . The Perrin numbers, named after the French engineer , bear ...

happy number In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy ...

, prime index prime and a strictly non-palindromic number.

368

368=2^4\times 23.

It is also a Leyland number.

369

References

Sources

* Wells, D. (1987). ''The Penguin Dictionary of Curious and Interesting Numbers'' (p. 152). London: Penguin Group.

External links

* {{Integers, 3 Integers