\|- \| colspan="2" \| \|- \| Cardinal \| 8 eight \|- \| Ordinal \| 8th eighth \|- \| Numeral system \| octal \|- \| Factorization \| $2^3$ \|- \| Divisors \| 1, 2, 4, 8 \|- \| Roman numeral \| VIII \|- \| Roman numeral (Unicode) \| Ⅷ, ⅷ \|- \| Arabic \|\| ٨ \|- \| Bengali \|\| ৮ \|- \| Chinese numeral \|\| 八 \|- \| Devanāgarī \|\| ८ \|- \| Hebrew \|\| ח (Het) \|- \| Khmer \|\| ៨ \|- \| prefixes \| octa-/oct- (from Greek) octo-/oct- (from Latin) \|- \| Binary \| 1000 \|- \| Octal \| 10 \|- \| Duodecimal \| 8 \|- \| Hexadecimal \| 8

8 (eight) is the natural number following 7 and preceding 9. The SI prefix for 1000⁸ is yotta (Y), and for its reciprocal yocto (y).

In mathematics

8 is a composite number, its proper divisors being 1, 2, and 4.
Eight is a power of two, being

2^3

, or two cubed. It has an aliquot sum of 7. All powers of 2 have an aliquot sum of one less than themselves.

8 is the base of the octal number system, which is mostly used with computers. In octal, one digit represents 3 bits. In modern computers, a byte is a grouping of eight bits, also called an octet.

The number 8 is a Fibonacci number, being 3 plus 5. The next Fibonacci number is 13.

8 and 9 form a Ruth-Aaron pair under the second definition in which repeated prime factors are counted as often as they occur.

A polygon with eight sides is an octagon. Figurate numbers representing octagons (including eight) are called octagonal numbers. A polyhedron with eight faces is an octahedron.

Sphenic numbers always have exactly eight divisors.

8 is the dimension of the octonions and is the highest possible dimension of a normed division algebra.

The number 8 is involved with a number of interesting mathematical phenomena related to the notion of Bott periodicity. For example if

O(\infty)

is the direct limit of the inclusions of real orthogonal groups

O(1)\hookrightarrow O(2)\hookrightarrow\ldots\hookrightarrow O(k)\hookrightarrow\ldots

then

\pi_{k+8}(O(\infty))\cong\pi_{k}(O(\infty))

. Clifford algebras also display a periodicity of 8. For example the algebra

Cl(p+8,q)

is isomorphic to the algebra of 16 by 16 matrices with entries in

Cl(p,q)

. We also see a period of 8 in the K theory of spheres and in the representation theory of the rotation groups, the latter giving rise to the 8 by 8 spinorial chessboard. All of these properties are closely related to the properties of the octonions.

The lowest dimensional even unimodular lattice is the 8-dimensional E₈ lattice. Even positive definite unimodular lattice exist only in dimensions divisible by 8.

A figure 8 is the common name of a geometric shape, often used in the context of sports, such as skating

In binary code eight is 1000; in ternary code eight is 22; in quaternary numeral system code eight is 20; in quinary eight is 13; in senary eight is 12; in septenary eight is 11; in octal eight is 10; in novenary code and all codes above (such as decimal and hexadecimal) eight is 8.

A fallen or lying down 8 (∞, the lemniscate) is used to represent infinity in mathematics. This interpretation of 8 may be related to the representation of the caduceus (where two snakes form several figure eights) as stability or balance of opposing forces.

Eight is the number of Thurston model geometries.

''E''₈ has rank 8.

\|- ! Base !! Numeral system \|- \| 2 \|\| binary \|\| 1000 \|- \| 3 \|\| ternary \|\| 22 \|- \| 4 \|\| quaternary \|\| 20 \|- \| 5 \|\| quinary \|\| 13 \|- \| 6 \|\| senary \|\| 12 \|- \| 7 \|\| septenary \|\| 11 \|- \| 8 \|\| octal \|\| 10 \|- \| colspan=2 \| over 8 (decimal, hexadecimal) \|\| 8

List of basic calculations

\|- !width="105px"\|Multiplication !1 !2 !3 !4 !5 !6 !7 !8 !9 !10 !width="5px"\| !11 !12 !13 !14 !15 !16 !17 !18 !19 !20 !width="5px"\| !21 !22 !23 !24 !25 !width="5px"\| !50 !100 !1000 \|- \| $8 \times x$ \|8 \|16 \|24 \|32 \|40 \|48 \|56 \|64 \|72 \|80 ! \|88 \|96 \|104 \|112 \|120 \|128 \|136 \|144 \|152 \|160 ! \|168 \|176 \|184 \|192 \|200 ! \|400 \|800 \|8000

\|- !width="105px"\|Division !1 !2 !3 !4 !5 !6 !7 !8 !9 !10 !width="5px"\| !11 !12 !13 !14 !15 \|- \| $8 \div x$ \|8 \|4 \| $2.\overline{6}$ \|2 \|1.6 \| $1.\overline{3}$ \| $1.\overline{142857}$ \|1 \| $0.\overline{8}$ \|0.8 ! \| $0.\overline{72}$ \| $0.\overline{6}$ \| $0.\overline{615384}$ \| $0.\overline{571428}$ \| $0.5\overline{3}$ \|- \| $x \div 8$ \|0.125 \|0.25 \|0.375 \|0.5 \|0.625 \|0.75 \|0.875 \|1 \|1.125 \|1.25 ! \|1.375 \|1.5 \|1.625 \|1.75 \|1.875

\|- !width="105px"\|Exponentiation !1 !2 !3 !4 !5 !6 !7 !8 !9 !10 !width="5px"\| !11 !12 !13 \|- \| $8 ^ x\,$ \|8 \|64 \|512 \|4096 \|32768 \|262144 \|2097152 \|16777216 \|134217728 \|1073741824 ! \|8589934592 \|68719476736 \|549755813888 \|- \| $x ^ 8\,$ \|1 \|256 \|6561 \|65536 \|390625 \|1679616 \|5764801 \|16777216 \|43046721 \|100000000 ! \|214358881 \|429981696 \|815730721

!rowspan="2" width="105px"\|Radix !1 !5 !10 !15 !20 !25 !30 !40 !50 !60 !70 !80 !90 !100 \|- !110 !120 !130 !140 !150 !200 !250 !500 !1000 !10000 !100000 !1000000 \| \| \|- \|rowspan="2"\| $x_{8} \$ \|1 \|5 \| $12_{8} \$ \| $17_{8} \$ \| $24_{8} \$ \| $31_{8} \$ \| $36_{8} \$ \| $50_{8} \$ \| $62_{8} \$ \| $74_{8} \$ \| $106_{8} \$ \| $120_{8} \$ \| $132_{8} \$ \| $144_{8} \$ \|- \| $156_{8} \$ \| $170_{8} \$ \| $202_{8} \$ \| $214_{8} \$ \| $226_{8} \$ \| $310_{8} \$ \| $372_{8} \$ \| $764_{8} \$ \| $1750_{8} \$ \| $23420_{8} \$ \| $303240_{8} \$ \| $3641100_{8} \$

Evolution of the glyph

In the beginning, various groups in India wrote eight more or less in one stroke as a curve that looks like an uppercase H with the bottom half of the left line and the upper half of the right line removed. At one point this glyph came close to looking like our modern five. With the western Ghubar Arabs, the similarity of the glyph to five was banished by connecting the beginning and the end of stroke together, and it was only a matter of the Europeans rounding the glyph that led to our modern eight.

Just as in most modern typefaces, in typefaces with text figures the 8 character usually has an ascender, as, for example, in . The "1" and "4" are old-style figures; the "8" is the same height in both old-style and modern figures. 1234567890 are all the same height; they are modern figures.

Astronomy

Messier object M8, a magnitude 5.0 nebula in the constellation of Sagittarius.

The New General Catalogue object NGC 8, a double star in the constellation Pegasus

The Saros number of the solar eclipse series which began on 2579 BCE March 7 and ended on 1281 BCE April 26. The duration of Saros series 8 was 1298.1 years, and it contained 73 solar eclipses.

The Saros number of the lunar eclipse series which began on 2512 BCE July 27 and ended on 961 BCE February 13. The duration of Saros series 7 was 1550.6 years, and it contained 87 lunar eclipses.

As of 2006, in our solar system, eight of the bodies orbiting the Sun are considered to be planets.

In religion

The Jewish religious rite of brit milah is held on a baby boy's eighth day of life

Hanukkah is an eight-day Jewish holiday that starts on the 25th day of Kislev

Shemini Atzeret (Hebrew: "Eighth Day of Assembly") is a one-day Jewish holiday immediately following the seven-day holiday of Sukkot

The Noble Eightfold Path in the Buddhist faith has eight steps

The Eight Immortals are Chinese deities

Members of The Church of Jesus Christ of Latter-day Saints believe that humans are responsible for their actions by the age of 8. Before that age, children lack sufficient knowledge to commit sin and are therefore exempt from judgment for their actions.

The Dharmachakra, a Buddhist symbol, has eight spokes. The Buddha's principal teaching -- the Four Noble Truths -- ramifies as the Eightfold Noble Path. In Mahayana Buddhism, the branches of the Eightfold Path are embodied by the Eight Great Bodhisattvas (Manjushri, Vajrapani, Avalokiteshvara, Maitreya, Kshitigarbha, Nivaranavishkambhi, Akashagarbha, and Samantabhadra). These are later (controversially) associated with the Eight Consciousnesses according to the Yogachara school of thought: consciousness in the five senses, thought-consciousness, self-consciousness and unconsciousness-'consciousness' (alaya-vijñana). The 'irreversible' state of enlightenment, at which point a Bodhisattva goes on 'autopilot', is the Eight Ground or ''bhūmi''. In general, 'eight' seems to be an auspicious number for Buddhists, e.g., the 'eight auspicious symbols' (the jewel-encrusted parasol; the goldfish (always shown as a pair, e.g., the glyph of Pisces); the self-replenishing amphora; the white ''kamala'' lotus-flower; the white conch; the eternal (Celtic-style, infinitely looping) knot; the banner of imperial victory; the eight-spoked wheel that guides the ship of state, or that symbolizes the Buddha's teaching). Similarly, Buddha's birthday falls on the 8th day of the 4th month of the Chinese calendar.

In Christianity, it is allegoric to Christ's sacrifice on the cross and is the number of Beatitudes.

In Islam, It is the number of Angels carrying The Holy Throne of Allah in heavens

In Neopaganism, there are eight Sabbats, festivals, seasons, or spokes in the Wheel of the Year

In music

A note played for one-eighth the duration of a whole note is called an eighth note, or quaver

An octave, the interval between two notes with the same letter name (where one has double the frequency of the other), is so called because there are eight notes on a western scale between the two, including the notes themselves

There are eight notes in an octatonic scale

There are eight musicians in an octet

Albums with the number eight in their title include ''8'' by the Swedish band Arvingarna and ''The Meaning of 8'' by Minnesota indie rock band Cloud Cult

Dream Theater's eighth album ''Octavarium'' contains many different references to the number 8, including the number of songs and various aspects of the music and cover artwork

"Eight maids a-milking" is the gift on the eighth day of Christmas in the carol "The Twelve Days of Christmas"

The 8-track cartridge is a musical recording format

"#8" is the stagename of Slipknot vocalist Corey Taylor

In sports

In football, the number 8 has historically been the number of the Central Midfielder or Box to Box Midfielder the best example being Steven Gerrard, while in rugby union the number eight central back row position wears the 8 shirt. Similarly in baseball, in its numbering system used to record defensive plays, eight represents the center fielder's position. The Philadelphia Flyers once had a line called the Crazy Eights with Eric Lindros at center (88); Mark Recchi (8); and Brent Fedyk (18).

In chess, each side has eight pawns; see also Eight queens puzzle

Eight ball billiards is played with 15 balls; the black ball numbered 8 being the most important one. Magic 8 Ball is a randomized process of predicting the future or answering various questions, packaged to resemble this ball and often sold as a fortune-telling device.

In Rowing an eight refers to a sweep oar boat with eight rowers plus a coxswain.

In rugby union, the only position without a proper name is the Number 8, a forward position.

In literature

In Terry Pratchett's ''Discworld'' series, eight is a holy number and is considered taboo. Eight is not safe to be said by wizards on the Discworld and is the number of Bel-Shamharoth. Also, there are eight days in a Disc week and eight colours in a Disc spectrum, the eighth one being Octarine

Lewis Carroll's poem The Hunting of the Snark has 8 "fits" (cantos), which is noted in the full name "The Hunting of the Snark - ''An Agony, in Eight Fits''

8 apparitions appear to Macbeth in Act 4 scene 1 of Shakespeare's Macbeth as representations of the 8 descendants of Banquo

In slang

An Eighth is a common measurement of marijuana, meaning an eighth of an ounce

Referring to the shape of the numeral, eight was represented in bingo slang, before political correctness, as "One Fat Lady". Eighty-eight was "Two Fat Ladies"

The numeral "8" is sometimes used in writing to represent the syllable "ate", as in writing "H8" for "hate", or "congr8ulations" for "congratulations". Avril Lavigne's song "Sk8er Boi" uses this convention in the title. Often found on vanity plates

"Section 8" is common U.S. slang for "crazy", based on the U.S. military's Section 8 discharge for mentally unfit personnel

In Colombia and Venezuela, "volverse un ocho" (meaning to tie oneself in a figure 8) refers to getting in trouble or contradicting one's self.

In China, '8' is used in chat speak as a term for parting. This is due to the closeness in pronunciation of '8' (bā) and the English word 'bye'.

In Washington, DC, seductively patting the bed covers in a figure-eight pattern in an invitation for sexual relations.

In other fields

The ordinal adjective is ''octonary''

Eight babies delivered in one birth are called octuplets. The first set of eight surviving babies, the Louis-Chukwu Octuplets, were born in 1998

October was the eighth month in the Roman calendar; currently August is the eighth month

I-8 is the designation of the US interstate highway that runs from San Diego, California to Casa Grande, Arizona

Eight is the number of categories the VALS system uses to classify consumer groups, and the number of categories used by Fallon-McElligott's system for teen marketing

War of the Eight Princes, a war in Chinese history

"88" is the abbreviated terminology used by the Aryan Brotherhood for the Nazi salute, Heil Hitler — "H" being the eighth letter of the alphabet, twice

The silver piece of eight was coined in the Spanish Empire and moved trade around the world

There are Eight Principles of Yong in Chinese calligraphy

8 is the number of days one can expect to wait for approval on Devilshire.

8 is one of the "Lost Numbers" on the television show, ''Lost'', along with 4, 15, 16, 23, and 42

In ''Stargate SG-1'' and ''Stargate Atlantis'', dialing an 8-chevron address will open a wormhole to another galaxy.

8vo is shorthand for "octavo", a book size.

The number of worlds in Super Mario Bros. and on Super Mario Bros. 3 (not counting the Warp World that is accessed by using a Toot Whistle).

Axel from Kingdom Hearts II is the eighth member of the Organization XIII.