Number

360

360 — Degrees in a Circle

360 is a composite number, even, a calendar year.

Three hundred sixty is the number of degrees in a full turn. The Babylonians chose it because it is divisible by every integer from 1 to 10 except 7.

Sources https://en.wikipedia.org/wiki/360_(number)

Abundant Number Curated Evil Number Gapful Number Harshad / Niven Highly Abundant Highly Composite Number Practical Number Preferred Number Recamán's Sequence Refactorable Number Semiperfect Number

Interestingness

★ ★ ★ ★ ★

9 notable facts · grade A

348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372

less more

Historical context — 360 AD

Calendar year

Year 360 (CCCLX) was a leap year starting on Saturday of the Julian calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 Read the full article on Wikipedia →

Historical context — 360 BC

Calendar year

Year 360 BC was a year of the pre-Julian Roman calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 Read the full article on Wikipedia →

Year facts

Year type: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 52
Started on: Friday
January 1, 360
Ended on: Saturday
December 31, 360
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 360s
360–369
Century: 4th century
301–400
Millennium: 1st millennium
1–1000
Years ago: 1,666
1666 years before 2026.

In other calendars

Hebrew: 4120 / 4121 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Metal zodiac:Monkey
Sexagenary cycle position 57 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 903 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 352 / 353 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 282 / 281 Saka
Indian national calendar; year starts in March.

Cultural significance

Western/Babylonian significant

Degrees in a full circle.

Babylonian base-60; conveniently divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12.

Sourced from Wikipedia (Numerology, Chinese numerology, Gematria, and per-culture articles).

Properties

Parity: Even
Digit count: 3
Digit sum: 9
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 9 bits
Reversed: 63
Recamán's sequence: a(528) = 360
Square (n²): 129,600
Cube (n³): 46,656,000
Divisor count: 24
σ(n) — sum of divisors: 1,170
φ(n) — Euler's totient: 96
Sum of prime factors: 17

Primality

Prime factorization: 2 ³ × 3 ² × 5

Nearest primes: 359 (−1) · 367 (+7)

Divisors & multiples

All divisors (24)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 9 · 10 · 12 · 15 · 18 · 20 · 24 · 30 · 36 · 40 · 45 · 60 · 72 · 90 · 120 · 180 (half) · 360

Aliquot sum (sum of proper divisors): 810

Factor pairs (a × b = 360)

1 × 360

2 × 180

3 × 120

4 × 90

5 × 72

6 × 60

8 × 45

9 × 40

10 × 36

12 × 30

15 × 24

18 × 20

First multiples

360 · 720 (double) · 1,080 · 1,440 · 1,800 · 2,160 · 2,520 · 2,880 · 3,240 · 3,600

Sums & aliquot sequence

As a sum of two squares: 6² + 18²

As consecutive integers: 119 + 120 + 121 70 + 71 + 72 + 73 + 74 36 + 37 + … + 44 17 + 18 + … + 31

Aliquot sequence: 360 → 810 → 1,368 → 2,532 → 3,404 → 2,980 → 3,320 → 4,240 → 5,804 → 4,360 → 5,540 → 6,136 → 6,464 → 6,490 → 6,470 → 5,194 → 4,040 — unresolved within range

Continued fraction of √n

√360 = [18; (1, 36)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: three hundred sixty
Ordinal: 360th
Roman numeral: CCCLX
Binary: 101101000
Octal: 550
Hexadecimal: 0x168
Base64: AWg=
One's complement: 65,175 (16-bit)
Scientific notation: 3.6 × 10²
As a duration: 360 s = 6 minutes

In other bases

ternary (3) 111100

quaternary (4) 11220

quinary (5) 2420

senary (6) 1400

septenary (7) 1023

nonary (9) 440

undecimal (11) 2a8

duodecimal (12) 260

tridecimal (13) 219

tetradecimal (14) 1ba

pentadecimal (15) 190

As an angle

360° = 1 × 360°

0° ≈ 0 rad

Compass bearing: N (north)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓍢𓍢𓍢𓎆𓎆𓎆𓎆𓎆𓎆
Greek (Milesian): τξʹ
Mayan (base 20): 𝋲·𝋠
Chinese: 三百六十
Chinese (financial): 參佰陸拾

In other modern scripts

Eastern Arabic ٣٦٠ Devanagari ३६० Bengali ৩৬০ Tamil ௩௬௦ Thai ๓๖๐ Tibetan ༣༦༠ Khmer ៣៦០ Lao ໓໖໐ Burmese ၃၆၀

Digit at this position in famous constants

π — Pi (π): Digit 360 = 6
e — Euler's number (e): Digit 360 = 0
φ — Golden ratio (φ): Digit 360 = 6
√2 — Pythagoras's (√2): Digit 360 = 2
ln 2 — Natural log of 2: Digit 360 = 3
γ — Euler-Mascheroni (γ): Digit 360 = 3

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 360, here are decompositions:

7 + 353 = 360
11 + 349 = 360
13 + 347 = 360
23 + 337 = 360
29 + 331 = 360
43 + 317 = 360
47 + 313 = 360
53 + 307 = 360

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Capital Letter U With Tilde

U+0168

Uppercase letter (Lu)

UTF-8 encoding: C5 A8 (2 bytes).

Lookup U+0168 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000168

RGB(0, 1, 104)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.1.104.

Address: 0.0.1.104
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.1.104

Unspecified address (0.0.0.0/8) — "this network" placeholder.

NANP area code 360

The number 360 is an active NANP area code (North American Numbering Plan).

Primary area: Olympia / Bellingham
Region: Washington
Country: United States

Most NANP area codes have multiple overlays in dense regions; the primary area listed is the historic/largest population center for this code.

Look up area code 360 ↗

Musical pitch

Heard as a frequency, 360 Hz is closest to:

Concert pitch (A4 = 440 Hz): F♯4 (370 Hz, -47¢ — about midway to F4)
Scientific pitch (C4 = 256 Hz): F♯4 (362 Hz, -10¢)
Baroque pitch (A4 = 415 Hz): G4 (369.7 Hz, -46¢ — about midway to F♯4)

Angle

360° is 2π radians — a full turn, all the way around.