Number

12

12 — The dozen

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

Twelve beat ten to most of the jobs that matter, and it won on divisibility. Twelve splits cleanly by 1, 2, 3, 4 and 6; ten manages only 1, 2 and 5. If you are dividing goods, hours or a circle among people, thirds and quarters come out whole in twelve and ragged in ten — which is why commerce, timekeeping and measurement all drifted towards it long before decimal notation won the argument.

The origin may be as close as your hand. Each finger other than the thumb has three bones, so a thumb tallying phalanges counts to twelve on one hand. Count twelves on one hand and fives on the other and you arrive at sixty — the Babylonian base that still rules clocks, minutes and degrees. From there: twelve months, twelve hours of daylight and twelve of night (an Egyptian inheritance), twelve inches, twelve pence to the shilling, a dozen, and a gross of 144.

Culture layered on top of the arithmetic — twelve apostles, twelve tribes of Israel, twelve Olympians, twelve imams, twelve signs of the zodiac. And twelve holds a small mathematical distinction: it is the smallest abundant number, the first integer whose proper divisors add to more than itself (1 + 2 + 3 + 4 + 6 = 16). The Dozenal Society is still, politely, arguing that we picked the wrong base.

Sources https://en.wikipedia.org/wiki/12_(number) · https://en.wikipedia.org/wiki/Duodecimal

Abundant Number Cube-Free Curated Evil Number Harshad / Niven Highly Abundant Highly Composite Number Padovan Number Pell Number Pentagonal Pernicious Number Perrin Number Practical Number Preferred Number Pronic / Oblong Recamán's Sequence Refactorable Number Semiperfect Number Zuckerman Number

Interestingness

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Historical context — 12 AD

Calendar year

AD 12 (XII) was a leap year starting on Friday of the Julian calendar.

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

Historical context — 12 BC

Calendar year

Year 12 BC was either a common year starting on Saturday, Sunday or Monday or a leap year starting on Sunday of the Julian calendar and a common year starting on Friday of the Proleptic 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: Sunday
January 1, 12
Ended on: Monday
December 31, 12
Friday the 13ths: 3
3 Friday the 13ths this year.
Decade: 10s
10–19
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 2,014
2014 years before 2026.

In other calendars

Hebrew: 3772 / 3773 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Water zodiac:Monkey
Sexagenary cycle position 9 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 555 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 4 / 5 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -66 / -67 Saka
Indian national calendar; year starts in March.

Cultural significance

Christian sacred

The twelve apostles; the twelve tribes of Israel.

Recurs throughout the Bible as a number of completeness.

Western significant

Twelve months, twelve zodiac signs, twelve hours on a clock.

Babylonian-derived duodecimal divisions of time and the heavens.

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

Properties

Parity: Even
Digit count: 2
Digit sum: 3
Digit product: 2
Digital root: 3
Palindrome: No
Bit width: 4 bits
Reversed: 21
Recamán's sequence: a(8) = 12
Square (n²): 144
Cube (n³): 1,728
Divisor count: 6
σ(n) — sum of divisors: 28
φ(n) — Euler's totient: 4
Sum of prime factors: 7

Primality

Prime factorization: 2 ² × 3

Nearest primes: 11 (−1) · 13 (+1)

Divisors & multiples

All divisors (6)

1 · 2 · 3 · 4 · 6 (half) · 12

Aliquot sum (sum of proper divisors): 16

Factor pairs (a × b = 12)

1 × 12

2 × 6

3 × 4

First multiples

12 · 24 (double) · 36 · 48 · 60 · 72 · 84 · 96 · 108 · 120

Sums & aliquot sequence

As consecutive integers: 3 + 4 + 5

Aliquot sequence: 12 → 16 → 15 → 9 → 4 → 3 → 1 → 0 — terminates at zero

Continued fraction of √n

√12 = [3; (2, 6)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: twelve
Ordinal: 12th
Roman numeral: XII
Binary: 1100
Octal: 14
Hexadecimal: 0xC
Base64: DA==
One's complement: 243 (8-bit)
Scientific notation: 1.2 × 10¹

In other bases

ternary (3) 110

quaternary (4) 30

quinary (5) 22

senary (6) 20

septenary (7) 15

nonary (9) 13

undecimal (11) 11

duodecimal (12) 10

tridecimal (13) c

tetradecimal (14) c

pentadecimal (15) c

As an angle

12°

12° ≈ 0.209 rad

Compass bearing: NNE (north-northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒌋𒁹𒁹
Egyptian hieroglyphic: 𓎆𓏺𓏺
Greek (Milesian): ιβʹ
Mayan (base 20): 𝋬
Chinese: 一十二
Chinese (financial): 壹拾貳

In other modern scripts

Eastern Arabic ١٢ Devanagari १२ Bengali ১২ Tamil ௧௨ Thai ๑๒ Tibetan ༡༢ Khmer ១២ Lao ໑໒ Burmese ၁၂

Digit at this position in famous constants

π — Pi (π): Digit 12 = 8
e — Euler's number (e): Digit 12 = 5
φ — Golden ratio (φ): Digit 12 = 4
√2 — Pythagoras's (√2): Digit 12 = 7
ln 2 — Natural log of 2: Digit 12 = 5
γ — Euler-Mascheroni (γ): Digit 12 = 0

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 12, here are decompositions:

5 + 7 = 12

ASCII character

As an ASCII codepoint, 12 is FF (form feed). ASCII control character.

Hex color

#00000C

RGB(0, 0, 12)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.12.

Address: 0.0.0.12
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.12

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

US numbered highway

Matches numbered highway designation:

I-12 — Baton Rouge to Slidell, LA.

Interstate 12 on Wikipedia ↗

Musical pitch

As a MIDI note number, 12 is C0 (16.4 Hz at concert pitch). (below the ~20 Hz floor of human hearing — likely inaudible)

Atomic number

On the periodic table, atomic number 12 is Magnesium (Mg) — period 3.

Magnesium on Wikipedia ↗

Time & calendar

12 is the number of months in a year, and the hours marked on a clock face.

Units of time — Wikipedia ↗