Natural number
Cardinal three hundred sixty
Ordinal 360th (three hundred sixtieth)
Factorization 23 × 32 × 5
Divisors 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
Greek numeral ΤΞ´
Roman numeral CCCLX
Binary 1011010002
Ternary 1111003
Senary 14006
Octal 5508
Duodecimal 26012
Hexadecimal 16816
The surface of the
compound of five cubes consists of 360 triangles.
360 (three hundred [and] sixty ) is the
natural number following
359 and preceding
361 .
In mathematics
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 a triangular matchstick number.
[2]
A
circle is divided into 360
degrees for
angular measurement . 360° = 2π
rad is also called a
round angle . This unit choice divides round angles into equal
sectors measured in integer rather than fractional degrees. Many angles commonly appearing in
planimetrics have an integer number of degrees. For a
simple non-intersecting
polygon , the sum of the
internal angles of a
quadrilateral always equals 360 degrees.
Integers from 361 to 369
361
361
=
19
2
,
{\displaystyle 361=19^{2},}
centered triangular number,
[4]
centered octagonal number ,
centered decagonal number ,
[5] member of the
Mian–Chowla sequence ;
[6] also the number of positions on a standard 19 × 19
Go board.
362
362
=
2
×
181
=
σ
2
(
19
)
{\displaystyle 362=2\times 181=\sigma _{2}(19)}
: sum of squares of divisors of 19,
[7] Mertens function returns 0,
[8] nontotient, noncototient.
[9]
363
364
364
=
2
2
×
7
×
13
{\displaystyle 364=2^{2}\times 7\times 13}
,
tetrahedral number ,
[10] sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0,
[11]
nontotient .
It is a
repdigit in
bases three (111111),
nine (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
tetrahedral number .
[12]
365
366
366
=
2
×
3
×
61
,
{\displaystyle 366=2\times 3\times 61,}
sphenic number ,
[13] Mertens function returns 0,
[14] noncototient,
[15] number of complete partitions of 20,
[16] 26-gonal and 123-gonal. There are also 366 days in a
leap year .
367
367 is a prime number,
Perrin number ,
[17]
happy number ,
prime index prime and a strictly non-palindromic number.
368
368
=
2
4
×
23.
{\displaystyle 368=2^{4}\times 23.}
It is also a
Leyland number .
[18]
369
References
^
Sloane, N. J. A. (ed.).
"Sequence A002182 (Highly composite numbers, definition (1): numbers n where d(n), the number of divisors of n (A000005), increases to a record.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-31 .
^
Sloane, N. J. A. (ed.).
"Sequence A045943 (Triangular matchstick numbers: a(n) is 3*n*(n+1)/2)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A002827 (Unitary perfect numbers: numbers k such that usigma(k) - k equals k.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-02 .
^
"Centered Triangular Number" . mathworld.wolfram.com .
^
Sloane, N. J. A. (ed.).
"Sequence A062786 (Centered 10-gonal numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-22 .
^
Sloane, N. J. A. (ed.).
"Sequence A005282 (Mian-Chowla sequence)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-22 .
^
Sloane, N. J. A. (ed.).
"Sequence A001157 (a(n) = sigma_2(n): sum of squares of divisors of n)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A028442 (Numbers k such that Mertens's function M(k) (A002321) is zero)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
"Noncototient" . mathworld.wolfram.com .
^
Sloane, N. J. A. (ed.).
"Sequence A000292 (Tetrahedral numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-22 .
^
Sloane, N. J. A. (ed.).
"Sequence A028442 (Numbers k such that Mertens's function M(k) (A002321) is zero)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A000292 (Tetrahedral (or triangular pyramidal) numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
"Sphenic number" . mathworld.wolfram.com .
^
Sloane, N. J. A. (ed.).
"Sequence A028442 (Numbers k such that Mertens's function M(k) (A002321) is zero)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
"Noncototient" . mathworld.wolfram.com .
^
Sloane, N. J. A. (ed.).
"Sequence A126796 (Number of complete partitions of n)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
"Parrin number" . mathworld.wolfram.com .
^
Sloane, N. J. A. (ed.).
"Sequence A076980" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
Sources
Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (p. 152). London: Penguin Group.
External links
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