Number

6

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

6 (six) is an even 1-digit number. It is a composite number with 4 divisors, and factors as 2 × 3. Remarkably, it is a perfect number: the sum of its proper divisors is exactly 6, equal to the number itself — a property shared by only a handful of known integers. It is the third triangular number and a factorial (3! = 6). Written other ways, in Roman numerals it is VI and in binary, 110.

Arithmetic Number Automorphic Number Cube-Free Evil Number Factorial Flippable Harshad / Niven Hexagonal Highly Abundant Highly Composite Number Lucky Number Narcissistic / Armstrong Octahedral Number Pentagonal Pyramidal Perfect Number Pernicious Number Practical Number Pronic / Oblong Recamán's Sequence Semiperfect Number Semiprime Squarefree Triangular Year Zuckerman Number

Interestingness

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22 notable facts · grade A

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Historical context — 6 AD

First 9 years of the Common Era

The 0s began on January 1, AD 1 and ended on December 31, AD 9, covering the first nine years of the Common Era.

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

Historical context — 6 BC

Calendar year

Year 6 BC was a common year starting on Sunday or Monday 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: Common year
Standard 365-day year; not divisible by 4 (or divisible by 100 but not 400).
Days in year: 365
ISO weeks: 52
Started on: Sunday
January 1, 6
Ended on: Sunday
December 31, 6
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 0s
0–9
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 2,020
2020 years before 2026.

In other calendars

Hebrew: 3766 / 3767 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Fire zodiac:Tiger
Sexagenary cycle position 3 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 549 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: -2 / -1 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -72 / -73 Saka
Indian national calendar; year starts in March.

Cultural significance

Chinese lucky

Lucky — "smooth" or "everything goes well."

六 (liù) sounds like 流 (liú, "flow/smooth").

Wikipedia ↗

Christian significant

The number of days of creation in Genesis.

Humanity created on the sixth day.

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

Properties

Parity: Even
Digit count: 1
Digit sum: 6
Digital root: 6
Palindrome: Yes
Bit width: 3 bits
Flips to (rotate 180°): 9
Recamán's sequence: a(3) = 6
Square (n²): 36
Cube (n³): 216
Divisor count: 4
σ(n) — sum of divisors: 12
φ(n) — Euler's totient: 2
Sum of prime factors: 5

Primality

Prime factorization: 2 × 3

Nearest primes: 5 (−1) · 7 (+1)

Divisors & multiples

All divisors (4)

1 · 2 · 3 (half) · 6

Aliquot sum (sum of proper divisors): 6

Factor pairs (a × b = 6)

1 × 6

2 × 3

First multiples

6 · 12 (double) · 18 · 24 · 30 · 36 · 42 · 48 · 54 · 60

Sums & aliquot sequence

As consecutive integers: 1 + 2 + 3

Aliquot sequence: 6 → 6 — reaches a perfect number

Continued fraction of √n

√6 = [2; (2, 4)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: six
Ordinal: 6th
Roman numeral: VI
Binary: 110
Octal: 6
Hexadecimal: 0x6
Base64: Bg==
One's complement: 249 (8-bit)

In other bases

ternary (3) 20

quaternary (4) 12

quinary (5) 11

senary (6) 10

septenary (7) 6

nonary (9) 6

undecimal (11) 6

duodecimal (12) 6

tridecimal (13) 6

tetradecimal (14) 6

pentadecimal (15) 6

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic: 𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian): ϛʹ
Mayan (base 20): 𝋦
Chinese: 六
Chinese (financial): 陸

In other modern scripts

Eastern Arabic ٦ Devanagari ६ Bengali ৬ Tamil ௬ Thai ๖ Tibetan ༦ Khmer ៦ Lao ໖ Burmese ၆

Digit at this position in famous constants

π — Pi (π): Digit 6 = 9
e — Euler's number (e): Digit 6 = 8
φ — Golden ratio (φ): Digit 6 = 3
√2 — Pythagoras's (√2): Digit 6 = 1
ln 2 — Natural log of 2: Digit 6 = 4
γ — Euler-Mascheroni (γ): Digit 6 = 1

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 6, here are decompositions:

3 + 3 = 6

ASCII character

As an ASCII codepoint, 6 is control character (0x06). ASCII control character.

Hex color

#000006

RGB(0, 0, 6)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.6.

Address: 0.0.0.6
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.6

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

Musical pitch

As a MIDI note number, 6 is F♯-1 (11.6 Hz at concert pitch). (below the ~20 Hz floor of human hearing — likely inaudible)

Atomic number

On the periodic table, atomic number 6 is Carbon (C) — period 2.

Carbon on Wikipedia ↗