# 360 (number)

 ← 359 360 361 →
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
Binary1011010002
Ternary1111003
Senary14006
Octal5508
Duodecimal26012

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]
• 360 is the product of the first two unitary perfect numbers:[3] ${\displaystyle 60\times 6=360.}$

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

${\displaystyle 361=19^{2},}$ centered triangular number,[4] centered octagonal number, centered decagonal number,[5] member of the Mian–Chowla sequence,[6]. There are also 361 positions on a standard 19 × 19 Go board.

### 362

${\displaystyle 362=2\times 181=\sigma _{2}(19)}$: sum of squares of divisors of 19,[7] Mertens function returns 0,[8] nontotient, noncototient.[9]

### 364

${\displaystyle 364=2^{2}\times 7\times 13}$, 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]

### 366

${\displaystyle 366=2\times 3\times 61,}$ 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

${\displaystyle 368=2^{4}\times 23.}$ It is also a Leyland number.[18]

## References

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.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
2. ^ 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.
3. ^ 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.
4. ^ "Centered Triangular Number". mathworld.wolfram.com.
5. ^ Sloane, N. J. A. (ed.). "Sequence A062786 (Centered 10-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
6. ^ Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
7. ^ 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.
8. ^
9. ^ "Noncototient". mathworld.wolfram.com.
10. ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
11. ^
12. ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral (or triangular pyramidal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
13. ^ "Sphenic number". mathworld.wolfram.com.
14. ^
15. ^ "Noncototient". mathworld.wolfram.com.
16. ^ Sloane, N. J. A. (ed.). "Sequence A126796 (Number of complete partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
17. ^ "Parrin number". mathworld.wolfram.com.
18. ^ 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.