Number

180

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

180 (one hundred eighty) is an even 3-digit number. It is a composite number with 18 divisors, and factors as 2² × 3² × 5. Its proper divisors sum to 366, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is CLXXX and in binary, 10110100.

Abundant Number Cube-Free Evil Number Flippable Gapful Number Harshad / Niven Highly Abundant Highly Composite Number Practical Number Preferred Number Recamán's Sequence Refactorable Number Semiperfect Number Year

Interestingness

★ ★ ★ ★ ★

11 notable facts · grade A

168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192

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Notable events — 180 AD

Mar 17 Emperor Marcus Aurelius dies; his son Commodus succeeds him.

Events compiled from Wikipedia ↗ · Licensed CC BY-SA 4.0

Historical context — 180 BC

Calendar year

Year 180 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: Saturday
January 1, 180
Ended on: Sunday
December 31, 180
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 180s
180–189
Century: 2nd century
101–200
Millennium: 1st millennium
1–1000
Years ago: 1,846
1846 years before 2026.

In other calendars

Hebrew: 3940 / 3941 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: 723 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 172 / 173 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 102 / 101 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 3
Digit sum: 9
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 8 bits
Reversed: 81
Flips to (rotate 180°): 81
Recamán's sequence: a(307) = 180
Square (n²): 32,400
Cube (n³): 5,832,000
Divisor count: 18
σ(n) — sum of divisors: 546
φ(n) — Euler's totient: 48
Sum of prime factors: 15

Primality

Prime factorization: 2 ² × 3 ² × 5

Nearest primes: 179 (−1) · 181 (+1)

Divisors & multiples

All divisors (18)

1 · 2 · 3 · 4 · 5 · 6 · 9 · 10 · 12 · 15 · 18 · 20 · 30 · 36 · 45 · 60 · 90 (half) · 180

Aliquot sum (sum of proper divisors): 366

Factor pairs (a × b = 180)

1 × 180

2 × 90

3 × 60

4 × 45

5 × 36

6 × 30

9 × 20

10 × 18

12 × 15

First multiples

180 · 360 (double) · 540 · 720 · 900 · 1,080 · 1,260 · 1,440 · 1,620 · 1,800

Sums & aliquot sequence

As a sum of two squares: 6² + 12²

As consecutive integers: 59 + 60 + 61 34 + 35 + 36 + 37 + 38 19 + 20 + … + 26 16 + 17 + … + 24

Aliquot sequence: 180 → 366 → 378 → 582 → 594 → 846 → 1,026 → 1,374 → 1,386 → 2,358 → 2,790 → 4,698 → 6,192 → 11,540 → 12,736 → 12,664 → 11,096 — unresolved within range

Continued fraction of √n

√180 = [13; (2, 2, 2, 26)]

Period length 4 — the block in parentheses repeats forever.

Representations

In words: one hundred eighty
Ordinal: 180th
Roman numeral: CLXXX
Binary: 10110100
Octal: 264
Hexadecimal: 0xB4
Base64: tA==
One's complement: 75 (8-bit)
Scientific notation: 1.8 × 10²
As a duration: 180 s = 3 minutes

In other bases

ternary (3) 20200

quaternary (4) 2310

quinary (5) 1210

senary (6) 500

septenary (7) 345

nonary (9) 220

undecimal (11) 154

duodecimal (12) 130

tridecimal (13) 10b

tetradecimal (14) cc

pentadecimal (15) c0

As an angle

180°

180° ≈ 3.142 rad

Compass bearing: S (south)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓍢𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆
Greek (Milesian): ρπʹ
Mayan (base 20): 𝋩·𝋠
Chinese: 一百八十
Chinese (financial): 壹佰捌拾

In other modern scripts

Eastern Arabic ١٨٠ Devanagari १८० Bengali ১৮০ Tamil ௧௮௦ Thai ๑๘๐ Tibetan ༡༨༠ Khmer ១៨០ Lao ໑໘໐ Burmese ၁၈၀

Digit at this position in famous constants

π — Pi (π): Digit 180 = 5
e — Euler's number (e): Digit 180 = 3
φ — Golden ratio (φ): Digit 180 = 3
√2 — Pythagoras's (√2): Digit 180 = 9
ln 2 — Natural log of 2: Digit 180 = 0
γ — Euler-Mascheroni (γ): Digit 180 = 7

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 180, here are decompositions:

7 + 173 = 180
13 + 167 = 180
17 + 163 = 180
23 + 157 = 180
29 + 151 = 180
31 + 149 = 180
41 + 139 = 180
43 + 137 = 180

Showing the first eight; more decompositions exist.

Unicode codepoint

Acute Accent

U+00B4

Modifier symbol (Sk)

UTF-8 encoding: C2 B4 (2 bytes).

Lookup U+00B4 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0000B4

RGB(0, 0, 180)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.180.

Address: 0.0.0.180
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.180

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

Geographic coordinate

As a geographic coordinate in degrees, this matches:

Antimeridian (longitude) — 180° longitude — the rough basis for the International Date Line in the Pacific.

World map (equirectangular projection) — Longitude 180° — Antimeridian

Calculator-display word

Type 180 on a seven-segment calculator, flip it 180°, and the display reads:

OBI

A staple of calculator humor since pocket calculators put digits in front of bored students.

Musical pitch

Heard as a frequency, 180 Hz is closest to:

Concert pitch (A4 = 440 Hz): F♯3 (185 Hz, -47¢ — about midway to F3)
Scientific pitch (C4 = 256 Hz): F♯3 (181 Hz, -10¢)
Baroque pitch (A4 = 415 Hz): G3 (184.9 Hz, -46¢ — about midway to F♯3)

Angle

180° is π radians — a straight angle (a half turn).