Movatterモバイル変換


[0]ホーム

URL:


Jump to content
WikipediaThe Free Encyclopedia
Search

360 (number)

From Wikipedia, the free encyclopedia
Natural number
← 359360 361 →
Cardinalthree hundred sixty
Ordinal360th
(three hundred sixtieth)
Factorization23 × 32 × 5
Divisors1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
Greek numeralΤΞ´
Roman numeralCCCLX,ccclx
Binary1011010002
Ternary1111003
Senary14006
Octal5508
Duodecimal26012
Hexadecimal16816
The surface of thecompound of five cubes consists of 360 triangles.

360 (three hundred [and] sixty) is thenatural number following359 and preceding361.

In mathematics

[edit]
  • 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, except7. Furthermore, one of the divisors of 360 is72, which is the number ofprimes below it.
  • 360 is a triangular matchstick number.[4]

Aturn is divided into 360degrees forangular measurement.360° = 2π rad is also called around angle. This unit choice divides round angles into equalsectors measured in integer rather than fractional degrees. Many angles commonly appearing inplanimetrics have an integer number of degrees. For asimple non-intersectingpolygon, the sum of theinternal angles of aquadrilateral always equals 360 degrees.

Integers from 361 to 369

[edit]

361

[edit]

361=192,{\displaystyle 361=19^{2},} centered triangular number,[6]centered octagonal number,centered decagonal number,[7] member of theMian–Chowla sequence.[8] There are also 361 positions on a standard 19 × 19Go board.

362

[edit]

362=2×181=σ2(19){\displaystyle 362=2\times 181=\sigma _{2}(19)}: sum of squares of divisors of 19,[9] Mertens function returns 0,[10] nontotient, noncototient.[11]

363

[edit]
Main article:363 (number)

364

[edit]

364=22×7×13{\displaystyle 364=2^{2}\times 7\times 13},tetrahedral number,[12] sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0,[10]nontotient.

It is arepdigit inbases 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-zerotetrahedral number.[13]

365

[edit]
Main article:365 (number)

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

366

[edit]

366=2×3×61,{\displaystyle 366=2\times 3\times 61,}sphenic number,[14] Mertens function returns 0,[10] noncototient,[11] number of complete partitions of 20,[15] 26-gonal and 123-gonal. There are also 366 days in aleap year.

367

[edit]

367 is a prime number,Perrin number,[16]happy number,prime index prime and a strictly non-palindromic number.

368

[edit]

368=24×23.{\displaystyle 368=2^{4}\times 23.} It is also aLeyland number.[17]

369

[edit]
Main article:369 (number)

References

[edit]
  1. ^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.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-31.
  2. ^"A002201 - OEIS".oeis.org. Retrieved2024-11-28.
  3. ^"A004490 - OEIS".oeis.org. Retrieved2024-11-28.
  4. ^Sloane, N. J. A. (ed.)."Sequence A045943 (Triangular matchstick numbers: a(n) is 3*n*(n+1)/2)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^Sloane, N. J. A. (ed.)."Sequence A002827 (Unitary perfect numbers: numbers k such that usigma(k) - k equals k.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2023-11-02.
  6. ^"Centered Triangular Number".mathworld.wolfram.com.
  7. ^Sloane, N. J. A. (ed.)."Sequence A062786 (Centered 10-gonal numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-22.
  8. ^Sloane, N. J. A. (ed.)."Sequence A005282 (Mian-Chowla sequence)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-22.
  9. ^Sloane, N. J. A. (ed.)."Sequence A001157 (a(n) = sigma_2(n): sum of squares of divisors of n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^abcSloane, N. J. A. (ed.)."Sequence A028442 (Numbers k such that Mertens's function M(k) (A002321) is zero)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. ^ab"Noncototient".mathworld.wolfram.com.
  12. ^Sloane, N. J. A. (ed.)."Sequence A000292 (Tetrahedral numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-22.
  13. ^Sloane, N. J. A. (ed.)."Sequence A000292 (Tetrahedral (or triangular pyramidal) numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  14. ^"Sphenic number".mathworld.wolfram.com.
  15. ^Sloane, N. J. A. (ed.)."Sequence A126796 (Number of complete partitions of n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  16. ^"Parrin number".mathworld.wolfram.com.
  17. ^Sloane, N. J. A. (ed.)."Sequence A076980".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
This article includes a list ofgeneral references, butit lacks sufficient correspondinginline citations. Please help toimprove this article byintroducing more precise citations.(April 2011) (Learn how and when to remove this message)

Sources

[edit]
  • Wells, D. (1987).The Penguin Dictionary of Curious and Interesting Numbers (p. 152). London: Penguin Group.

External links

[edit]
0 to 199
200 to 399
400 to 999
1000s and 10,000s
1000s
10,000s
100,000s to 10,000,000,000,000s
Retrieved from "https://en.wikipedia.org/w/index.php?title=360_(number)&oldid=1317388361"
Category:
Hidden categories:

[8]ページ先頭

©2009-2025 Movatter.jp