Number

1,080

1,080 is a composite number, even, a calendar year.

1,080 (one thousand eighty) is an even 4-digit number. It is a composite number with 32 divisors, and factors as 2³ × 3³ × 5. Its proper divisors sum to 2,520, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MLXXX and in binary, 10000111000.

Abundant Number Evil Number Flippable Gapful Number Harshad / Niven Highly Abundant Pentagonal Practical Number Recamán's Sequence Semiperfect Number Year

Interestingness

★ ★ ★ ★ ★

8 notable facts · grade A

1,068 1,069 1,070 1,071 1,072 1,073 1,074 1,075 1,076 1,077 1,078 1,079 1,080 1,081 1,082 1,083 1,084 1,085 1,086 1,087 1,088 1,089 1,090 1,091 1,092

less more

Historical context — 1080 AD

Calendar year

Year 1080 (MLXXX) was a leap year starting on Wednesday of the Julian 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: 53
Long year: contains 53 ISO weeks.
Started on: Thursday
January 1, 1080
Ended on: Friday
December 31, 1080
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 1080s
1080–1089
Century: 11th century
1001–1100
Millennium: 2nd millennium
1001–2000
Years ago: 946
946 years before 2026.

In other calendars

Hebrew: 4840 / 4841 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 472 / 473 AH
Lunar calendar; year spans differ from Gregorian.
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: 1623 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 458 / 459 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1072 / 1073 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1002 / 1001 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 4
Digit sum: 9
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 11 bits
Reversed: 801
Flips to (rotate 180°): 801
Recamán's sequence: a(4,259) = 1,080
Square (n²): 1,166,400
Cube (n³): 1,259,712,000
Divisor count: 32
σ(n) — sum of divisors: 3,600
φ(n) — Euler's totient: 288
Sum of prime factors: 20

Primality

Prime factorization: 2 ³ × 3 ³ × 5

Nearest primes: 1,069 (−11) · 1,087 (+7)

Divisors & multiples

All divisors (32)

1 · 2 · 3 · 4 · 5 · 6 · 8 · 9 · 10 · 12 · 15 · 18 · 20 · 24 · 27 · 30 · 36 · 40 · 45 · 54 · 60 · 72 · 90 · 108 · 120 · 135 · 180 · 216 · 270 · 360 · 540 (half) · 1080

Aliquot sum (sum of proper divisors): 2,520

Factor pairs (a × b = 1,080)

1 × 1080

2 × 540

3 × 360

4 × 270

5 × 216

6 × 180

8 × 135

9 × 120

10 × 108

12 × 90

15 × 72

18 × 60

20 × 54

24 × 45

27 × 40

30 × 36

First multiples

1,080 · 2,160 (double) · 3,240 · 4,320 · 5,400 · 6,480 · 7,560 · 8,640 · 9,720 · 10,800

Sums & aliquot sequence

As consecutive integers: 359 + 360 + 361 214 + 215 + 216 + 217 + 218 116 + 117 + … + 124 65 + 66 + … + 79

Aliquot sequence: 1,080 → 2,520 → 6,840 → 16,560 → 41,472 → 82,311 → 27,441 → 12,209 → 451 → 53 → 1 → 0 — terminates at zero

Continued fraction of √n

√1,080 = [32; (1, 6, 3, 6, 1, 64)]

Period length 6 — the block in parentheses repeats forever.

Representations

In words: one thousand eighty
Ordinal: 1080th
Roman numeral: MLXXX
Binary: 10000111000
Octal: 2070
Hexadecimal: 0x438
Base64: BDg=
One's complement: 64,455 (16-bit)
Scientific notation: 1.08 × 10³
As a duration: 1,080 s = 18 minutes

In other bases

ternary (3) 1111000

quaternary (4) 100320

quinary (5) 13310

senary (6) 5000

septenary (7) 3102

nonary (9) 1430

undecimal (11) 8a2

duodecimal (12) 760

tridecimal (13) 651

tetradecimal (14) 572

pentadecimal (15) 4c0

As an angle

1,080° = 3 × 360°

0° ≈ 0 rad

Compass bearing: N (north)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓆼𓎆𓎆𓎆𓎆𓎆𓎆𓎆𓎆
Greek (Milesian): ͵απʹ
Mayan (base 20): 𝋢·𝋮·𝋠
Chinese: 一千零八十
Chinese (financial): 壹仟零捌拾

In other modern scripts

Eastern Arabic ١٠٨٠ Devanagari १०८० Bengali ১০৮০ Tamil ௧௦௮௦ Thai ๑๐๘๐ Tibetan ༡༠༨༠ Khmer ១០៨០ Lao ໑໐໘໐ Burmese ၁၀၈၀

Digit at this position in famous constants

π — Pi (π): Digit 1,080 = 9
e — Euler's number (e): Digit 1,080 = 0
φ — Golden ratio (φ): Digit 1,080 = 5
√2 — Pythagoras's (√2): Digit 1,080 = 3
ln 2 — Natural log of 2: Digit 1,080 = 2
γ — Euler-Mascheroni (γ): Digit 1,080 = 7

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1080, here are decompositions:

11 + 1069 = 1080
17 + 1063 = 1080
19 + 1061 = 1080
29 + 1051 = 1080
31 + 1049 = 1080
41 + 1039 = 1080
47 + 1033 = 1080
59 + 1021 = 1080

Showing the first eight; more decompositions exist.

Unicode codepoint

Cyrillic Small Letter I

U+0438

Lowercase letter (Ll)

UTF-8 encoding: D0 B8 (2 bytes).

Lookup U+0438 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#000438

RGB(0, 4, 56)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.4.56.

Address: 0.0.4.56
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.4.56

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

Musical pitch

Heard as a frequency, 1,080 Hz is closest to:

Concert pitch (A4 = 440 Hz): C♯6 (1108.7 Hz, -45¢ — about midway to C6)
Scientific pitch (C4 = 256 Hz): C♯6 (1084.9 Hz, -8¢)
Baroque pitch (A4 = 415 Hz): D6 (1107.9 Hz, -44¢)

Position in π

The digit sequence 1080 first appears in π at position 11,601 of the decimal expansion (the 11,601ordinal-suffix:st digit after the integer 3).

Search range: the first 1,000,000 fractional digits of π. Any 6-digit-or-shorter string is virtually guaranteed to appear in there — the more interesting signal is the position.

Look up 1080 on Pi Search ↗