Number

2,016

2,016 is a composite number, even, a calendar year.

2,016 (two thousand sixteen) is an even 4-digit number. It is a composite number with 36 divisors, and factors as 2⁵ × 3² × 7. Its proper divisors sum to 4,536, more than the number itself, making it an abundant number. It is the 63rd triangular number. Written other ways, in Roman numerals it is MMXVI and in binary, 11111100000.

Abundant Number Arithmetic Number Evil Number Harshad / Niven Hexagonal Practical Number Recamán's Sequence Refactorable Number Semiperfect Number Triangular Year

Interestingness

★ ★ ★ ★ ★

8 notable facts · grade A

2,004 2,005 2,006 2,007 2,008 2,009 2,010 2,011 2,012 2,013 2,014 2,015 2,016 2,017 2,018 2,019 2,020 2,021 2,022 2,023 2,024 2,025 2,026 2,027 2,028

less more

Notable events — 2016 AD

Jun 12 A gunman kills 49 at the Pulse nightclub in Orlando.
Jun 23 The United Kingdom votes to leave the European Union — "Brexit".
Jul 6 Pokémon Go launches, kicking off a global augmented-reality craze.
Aug 5 The Summer Olympics open in Rio de Janeiro, the first held in South America.
Nov 2 The Chicago Cubs win the World Series, ending a 108-year drought.

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

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, 2016
Ended on: Saturday
December 31, 2016
Friday the 13ths: 1
One Friday the 13th this year.
Easter Sunday: March 27
Sunday, March 27, 2016
Decade: 2010s
2010–2019
Century: 21st century
2001–2100
Millennium: 3rd millennium
2001–3000
Years ago: 10
10 years before 2026.
US presidential election: Yes
US holds a presidential election in years divisible by 4 starting from 1788.
Summer Olympics: Yes

In other calendars

Hebrew: 5776 / 5777 AM
Rosh Hashanah falls in September/October.
Islamic Hijri: 1437 / 1438 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: 2559 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri: 1394 / 1395 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian: 2008 / 2009 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 1938 / 1937 Saka
Indian national calendar; year starts in March.
Japanese: Heisei 28
Reign-era counting from the start of each emperor's reign.

Properties

Parity: Even
Digit count: 4
Digit sum: 9
Digit product: 0
Digital root: 9
Palindrome: No
Bit width: 11 bits
Reversed: 6,102
Recamán's sequence: a(3,719) = 2,016
Square (n²): 4,064,256
Cube (n³): 8,193,540,096
Divisor count: 36
σ(n) — sum of divisors: 6,552
φ(n) — Euler's totient: 576
Sum of prime factors: 23

Primality

Prime factorization: 2 ⁵ × 3 ² × 7

Nearest primes: 2,011 (−5) · 2,017 (+1)

Divisors & multiples

All divisors (36)

1 · 2 · 3 · 4 · 6 · 7 · 8 · 9 · 12 · 14 · 16 · 18 · 21 · 24 · 28 · 32 · 36 · 42 · 48 · 56 · 63 · 72 · 84 · 96 · 112 · 126 · 144 · 168 · 224 · 252 · 288 · 336 · 504 · 672 · 1008 (half) · 2016

Aliquot sum (sum of proper divisors): 4,536

Factor pairs (a × b = 2,016)

1 × 2016

2 × 1008

3 × 672

4 × 504

6 × 336

7 × 288

8 × 252

9 × 224

12 × 168

14 × 144

16 × 126

18 × 112

21 × 96

24 × 84

28 × 72

32 × 63

36 × 56

42 × 48

First multiples

2,016 · 4,032 (double) · 6,048 · 8,064 · 10,080 · 12,096 · 14,112 · 16,128 · 18,144 · 20,160

Sums & aliquot sequence

As consecutive integers: 671 + 672 + 673 285 + 286 + … + 291 220 + 221 + … + 228 86 + 87 + … + 106

Aliquot sequence: 2,016 → 4,536 → 9,984 → 18,632 → 18,628 → 13,978 → 7,802 → 4,294 → 2,546 → 1,534 → 986 → 634 → 320 → 442 → 314 → 160 → 218 — unresolved within range

Continued fraction of √n

√2,016 = [44; (1, 8, 1, 88)]

Period length 4 — the block in parentheses repeats forever.

Representations

In words: two thousand sixteen
Ordinal: 2016th
Roman numeral: MMXVI
Binary: 11111100000
Octal: 3740
Hexadecimal: 0x7E0
Base64: B+A=
One's complement: 63,519 (16-bit)
Scientific notation: 2.016 × 10³
As a duration: 2,016 s = 33 minutes, 36 seconds

In other bases

ternary (3) 2202200

quaternary (4) 133200

quinary (5) 31031

senary (6) 13200

septenary (7) 5610

nonary (9) 2680

undecimal (11) 1573

duodecimal (12) 1200

tridecimal (13) bc1

tetradecimal (14) a40

pentadecimal (15) 8e6

As an angle

2,016° = 5 × 360° + 216°

216° ≈ 3.77 rad

Compass bearing: SW (southwest)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹𒁹𒁹 𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓆼𓆼𓎆𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ͵βιϛʹ
Mayan (base 20): 𝋥·𝋠·𝋰
Chinese: 二千零一十六
Chinese (financial): 貳仟零壹拾陸

In other modern scripts

Eastern Arabic ٢٠١٦ Devanagari २०१६ Bengali ২০১৬ Tamil ௨௦௧௬ Thai ๒๐๑๖ Tibetan ༢༠༡༦ Khmer ២០១៦ Lao ໒໐໑໖ Burmese ၂၀၁၆

Digit at this position in famous constants

π — Pi (π): Digit 2,016 = 6
e — Euler's number (e): Digit 2,016 = 9
φ — Golden ratio (φ): Digit 2,016 = 0
√2 — Pythagoras's (√2): Digit 2,016 = 6
ln 2 — Natural log of 2: Digit 2,016 = 3
γ — Euler-Mascheroni (γ): Digit 2,016 = 1

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 2016, here are decompositions:

5 + 2011 = 2016
13 + 2003 = 2016
17 + 1999 = 2016
19 + 1997 = 2016
23 + 1993 = 2016
29 + 1987 = 2016
37 + 1979 = 2016
43 + 1973 = 2016

Showing the first eight; more decompositions exist.

Unicode codepoint

Nko Letter Na Woloso

U+07E0

Other letter (Lo)

UTF-8 encoding: DF A0 (2 bytes).

Lookup U+07E0 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0007E0

RGB(0, 7, 224)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.7.224.

Address: 0.0.7.224
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.7.224

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

Musical pitch

Heard as a frequency, 2,016 Hz is closest to:

Concert pitch (A4 = 440 Hz): B6 (1975.5 Hz, +35¢)
Scientific pitch (C4 = 256 Hz): C7 (2048 Hz, -27¢)
Baroque pitch (A4 = 415 Hz): C7 (1974.1 Hz, +36¢)

Position in π

The digit sequence 2016 first appears in π at position 7,174 of the decimal expansion (the 7,174ordinal-suffix:th 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 2016 on Pi Search ↗