360 (number)

Last updated
359 360 361
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, 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. Compound of five cubes, gray and rgby.png
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.

Contents

In mathematics

A turn 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

centered triangular number, [6] centered octagonal number, centered decagonal number, [7] member of the Mian–Chowla sequence. [8] There are also 361 positions on a standard 19 × 19 Go board.

362

: sum of squares of divisors of 19, [9] Mertens function returns 0, [10] nontotient, noncototient. [11]

363

364

, 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 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. [13]

365

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

366

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 a leap year.

367

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

368

It is also a Leyland number. [17]

369

References

  1. Sloane, N. J. A. (ed.). "SequenceA002182(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.
  2. "A002201 - OEIS". oeis.org. Retrieved 2024-11-28.
  3. "A004490 - OEIS". oeis.org. Retrieved 2024-11-28.
  4. Sloane, N. J. A. (ed.). "SequenceA045943(Triangular matchstick numbers: a(n) is 3*n*(n+1)/2)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. Sloane, N. J. A. (ed.). "SequenceA002827(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.
  6. "Centered Triangular Number". mathworld.wolfram.com.
  7. Sloane, N. J. A. (ed.). "SequenceA062786(Centered 10-gonal numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-22.
  8. Sloane, N. J. A. (ed.). "SequenceA005282(Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-22.
  9. Sloane, N. J. A. (ed.). "SequenceA001157(a(n) = sigma_2(n): sum of squares of divisors of n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  10. 1 2 3 Sloane, N. J. A. (ed.). "SequenceA028442(Numbers k such that Mertens's function M(k) (A002321) is zero)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  11. 1 2 "Noncototient". mathworld.wolfram.com.
  12. Sloane, N. J. A. (ed.). "SequenceA000292(Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-22.
  13. Sloane, N. J. A. (ed.). "SequenceA000292(Tetrahedral (or triangular pyramidal) numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  14. "Sphenic number". mathworld.wolfram.com.
  15. Sloane, N. J. A. (ed.). "SequenceA126796(Number of complete partitions of n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  16. "Parrin number". mathworld.wolfram.com.
  17. Sloane, N. J. A. (ed.). "SequenceA076980". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.

Sources