Number

1,116

1,116 is a composite number, even, a calendar year.

1,116 (one thousand one hundred sixteen) is an even 4-digit number. It is a composite number with 18 divisors, and factors as 2² × 3² × 31. Its proper divisors sum to 1,796, more than the number itself, making it an abundant number. Written other ways, in Roman numerals it is MCXVI and in binary, 10001011100.

Abundant Number Cube-Free Flippable Harshad / Niven Odious Number Pernicious Number Practical Number Recamán's Sequence Refactorable Number Semiperfect Number Year Zuckerman Number

Interestingness

★ ★ ★ ★ ★

8 notable facts · grade A

1,104 1,105 1,106 1,107 1,108 1,109 1,110 1,111 1,112 1,113 1,114 1,115 1,116 1,117 1,118 1,119 1,120 1,121 1,122 1,123 1,124 1,125 1,126 1,127 1,128

less more

Historical context — 1116 AD

Calendar year

Year 1116 (MCXVI) 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 →

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, 1116
Ended on: Sunday
December 31, 1116
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 1110s
1110–1119
Century: 12th century
1101–1200
Millennium: 2nd millennium
1001–2000
Years ago: 910
910 years before 2026.

In other calendars

Hebrew: 4876 / 4877 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 509 / 510 AH
Lunar calendar; year spans differ from Gregorian.
Chinese: Year of the zodiac:Fire zodiac:Monkey
Sexagenary cycle position 33 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 1659 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 494 / 495 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 1108 / 1109 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1038 / 1037 Saka
Indian national calendar; year starts in March.

Properties

Parity: Even
Digit count: 4
Digit sum: 9
Digit product: 6
Digital root: 9
Palindrome: No
Bit width: 11 bits
Reversed: 6,111
Flips to (rotate 180°): 9,111
Recamán's sequence: a(1,940) = 1,116
Square (n²): 1,245,456
Cube (n³): 1,389,928,896
Divisor count: 18
σ(n) — sum of divisors: 2,912
φ(n) — Euler's totient: 360
Sum of prime factors: 41

Primality

Prime factorization: 2 ² × 3 ² × 31

Nearest primes: 1,109 (−7) · 1,117 (+1)

Divisors & multiples

All divisors (18)

1 · 2 · 3 · 4 · 6 · 9 · 12 · 18 · 31 · 36 · 62 · 93 · 124 · 186 · 279 · 372 · 558 (half) · 1116

Aliquot sum (sum of proper divisors): 1,796

Factor pairs (a × b = 1,116)

1 × 1116

2 × 558

3 × 372

4 × 279

6 × 186

9 × 124

12 × 93

18 × 62

31 × 36

First multiples

1,116 · 2,232 (double) · 3,348 · 4,464 · 5,580 · 6,696 · 7,812 · 8,928 · 10,044 · 11,160

Sums & aliquot sequence

As consecutive integers: 371 + 372 + 373 136 + 137 + … + 143 120 + 121 + … + 128 35 + 36 + … + 58

Aliquot sequence: 1,116 → 1,796 → 1,354 → 680 → 940 → 1,076 → 814 → 554 → 280 → 440 → 640 → 890 → 730 → 602 → 454 → 230 → 202 — unresolved within range

Continued fraction of √n

√1,116 = [33; (2, 2, 5, 1, 2, 16, 2, 1, 5, 2, 2, 66)]

Period length 12 — the block in parentheses repeats forever.

Representations

In words: one thousand one hundred sixteen
Ordinal: 1116th
Roman numeral: MCXVI
Binary: 10001011100
Octal: 2134
Hexadecimal: 0x45C
Base64: BFw=
One's complement: 64,419 (16-bit)
Scientific notation: 1.116 × 10³
As a duration: 1,116 s = 18 minutes, 36 seconds

In other bases

ternary (3) 1112100

quaternary (4) 101130

quinary (5) 13431

senary (6) 5100

septenary (7) 3153

nonary (9) 1470

undecimal (11) 925

duodecimal (12) 790

tridecimal (13) 67b

tetradecimal (14) 59a

pentadecimal (15) 4e6

Palindromic in base 5

As an angle

1,116° = 3 × 360° + 36°

36° ≈ 0.628 rad

Compass bearing: NE (northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆼𓍢𓎆𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ͵αριϛʹ
Mayan (base 20): 𝋢·𝋯·𝋰
Chinese: 一千一百一十六
Chinese (financial): 壹仟壹佰壹拾陸

In other modern scripts

Eastern Arabic ١١١٦ Devanagari १११६ Bengali ১১১৬ Tamil ௧௧௧௬ Thai ๑๑๑๖ Tibetan ༡༡༡༦ Khmer ១១១៦ Lao ໑໑໑໖ Burmese ၁၁၁၆

Digit at this position in famous constants

π — Pi (π): Digit 1,116 = 5
e — Euler's number (e): Digit 1,116 = 1
φ — Golden ratio (φ): Digit 1,116 = 6
√2 — Pythagoras's (√2): Digit 1,116 = 2
ln 2 — Natural log of 2: Digit 1,116 = 2
γ — Euler-Mascheroni (γ): Digit 1,116 = 0

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 1116, here are decompositions:

7 + 1109 = 1116
13 + 1103 = 1116
19 + 1097 = 1116
23 + 1093 = 1116
29 + 1087 = 1116
47 + 1069 = 1116
53 + 1063 = 1116
67 + 1049 = 1116

Showing the first eight; more decompositions exist.

Unicode codepoint

Cyrillic Small Letter Kje

U+045C

Lowercase letter (Ll)

UTF-8 encoding: D1 9C (2 bytes).

Lookup U+045C on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#00045C

RGB(0, 4, 92)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.4.92.

Address: 0.0.4.92
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.4.92

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

Musical pitch

Heard as a frequency, 1,116 Hz is closest to:

Concert pitch (A4 = 440 Hz): C♯6 (1108.7 Hz, +11¢)
Scientific pitch (C4 = 256 Hz): C♯6 (1084.9 Hz, +49¢ — about midway to D6)
Baroque pitch (A4 = 415 Hz): D6 (1107.9 Hz, +13¢)

Position in π

The digit sequence 1116 first appears in π at position 3,992 of the decimal expansion (the 3,992ordinal-suffix:nd 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 1116 on Pi Search ↗