# 4

 ← 3 4 5 →
Cardinalfour
Ordinal4th
(fourth)
Numeral systemquaternary
Factorization22
Divisors1, 2, 4
Greek numeralΔ´
Roman numeralIV
Roman numeral (unicode)Ⅳ, ⅳ
Greek prefixtetra-
Binary1002
Ternary113
Quaternary104
Quinary45
Senary46
Octal48
Duodecimal412
Vigesimal420
Base 36436
Greekδ (or Δ)
Arabic, Kurdish٤
Persian۴
Urdu
Ge'ez
Bengali
Chinese numeral四，亖，肆
Korean넷,사
Devanagari
Telugu
Malayalam
Tamil
Hebrewד
Khmer
Thai
Burmese

4 (four) is a number, numeral, and glyph. It is the natural number following 3 and preceding 5

## In mathematics

Four is the smallest composite number, its proper divisors being 1 and 2.

4 is the smallest squared prime (p2) and the only even number in this form. 4 is also the only square one more than a prime number.

A number is a multiple of 4 if its last two digits are a multiple of 4. For example, 1092 is a multiple of 4 because 92 = 4 × 23.

In addition, 2 + 2 = 2 × 2 = 22 = 4. Continuing the pattern in Knuth's up-arrow notation, 2 ↑↑ 2 = 2 ↑↑↑ 2 = 4, and so on, for any number of up arrows. (That is, 2 [n] 2 = 4 for every positive integer n, where a [n] b is the hyperoperation.)

A four-sided plane figure is a quadrilateral (quadrangle) which include kites, rhombi, rectangles and squares, sometimes also called a tetragon. A circle divided by 4 makes right angles and four quadrants. Because of it, four (4) is the base number of the plane (mathematics). Four cardinal directions, four seasons, the duodecimal system, and the vigesimal system are based on four.

A solid figure with four faces as well as four vertices is a tetrahedron, and 4 is the smallest possible number of faces (as well as vertices) of a polyhedron. The regular tetrahedron is the simplest Platonic solid. A tetrahedron, which can also be called a 3-simplex, has four triangular faces and four vertices. It is the only self-dual regular polyhedron.

Four-dimensional space is the highest-dimensional space featuring more than three convex regular figures:

Four-dimensional differential manifolds have some unique properties. There is only one differential structure on ℝn except when n = 4, in which case there are uncountably many.

The smallest non-cyclic group has four elements; it is the Klein four-group. Four is also the order of the smallest non-trivial groups that are not simple.

Four is the only integer n for which the (non trivial) alternating group An is not simple.

Four is the maximum number of dimensions of a real associative division algebra (the quaternions), by a theorem of Ferdinand Georg Frobenius.

The four-color theorem states that a planar graph (or, equivalently, a flat map of two-dimensional regions such as countries) can be colored using four colors, so that adjacent vertices (or regions) are always different colors.[1] Three colors are not, in general, sufficient to guarantee this. The largest planar complete graph has four vertices.

Lagrange's four-square theorem states that every positive integer can be written as the sum of at most four square numbers. Three are not always sufficient; 7 for instance cannot be written as the sum of three squares.

Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. 4x = y2z2.

Four is the highest degree general polynomial equation for which there is a solution in radicals.

The four fours game, there are known solutions for all integers from 0 to 880 (but not 881).[citation needed]

Other Languages
አማርኛ: አራት
Ænglisc: Fēower
العربية: 4 (عدد)
ܐܪܡܝܐ: 4 (ܡܢܝܢܐ)
অসমীয়া:
asturianu: Cuatro
Avañe'ẽ: Irundy
авар: Ункъо
Aymar aru: Pusi
azərbaycanca: 4 (ədəd)
تۆرکجه: ۴ (سایی)
Bân-lâm-gú: 4
Bislama: Fo
български: 4 (число)
བོད་ཡིག: ༤ (གྲངས་ཀ།)
bosanski: 4 (broj)
brezhoneg: Pevar
català: Quatre
Чӑвашла: 4 (хисеп)
Cebuano: 4 (numero)
čeština: 4 (číslo)
chiShona: Zvina
chiTumbuka: Vinayi
Cymraeg: Pedwar
dansk: 4 (tal)
Deitsch: Vier
Deutsch: Vier
eesti: Neli
Ελληνικά: 4 (αριθμός)
emiliàn e rumagnòl: 4 (nùmer)
español: Cuatro
Esperanto: 4 (nombro)
euskara: Lau
فارسی: ۴ (عدد)
føroyskt: 4 (tal)
français: 4 (nombre)
Fulfulde: Nayi
furlan: 4 (numar)
Gaeilge: 4 (uimhir)
galego: Catro
ГӀалгӀай: 4 (таьрахь)

ગુજરાતી:

хальмг: 4
한국어: 4
Hausa: 4
հայերեն: Չորս
hrvatski: Četiri
Bahasa Hulontalo: 4
Igbo: Anọ
Bahasa Indonesia: 4 (angka)
interlingua: 4 (numero)
Iñupiak: Sisamat
isiXhosa: Zine
íslenska: Fjórir
italiano: 4 (numero)
עברית: 4 (מספר)
ಕನ್ನಡ: ನಾಲ್ಕು
ქართული: 4 (რიცხვი)
Kirundi: Kane
Kiswahili: Nne
коми: 4 (нёль)
Kongo: 4 (ntalu)
Kreyòl ayisyen: 4 (nonm)
лакку: Мукьва
Latina: Quattuor
latviešu: 4 (skaitlis)
Lëtzebuergesch: Véier
lietuvių: 4 (skaičius)
Limburgs: Veer
lingála: Mínei
Luganda: Nnya
lumbaart: Nümar 4
magyar: 4 (szám)
македонски: 4 (број)
മലയാളം: 4 (അക്കം)
მარგალური: ოთხი
Bahasa Melayu: 4 (nombor)
Mìng-dĕ̤ng-ngṳ̄: 4
Nāhuatl: Nāhui
Na Vosa Vakaviti: Va
Nederlands: 4 (getal)
नेपाल भाषा:

Napulitano: Quatto
Nordfriisk: Fjouer
norsk: 4 (tall)
norsk nynorsk: Talet 4
ଓଡ଼ିଆ: ୪ (ସଂଖ୍ୟା)
oʻzbekcha/ўзбекча: 4 (son)
پنجابی: 4
پښتو: ۴
Перем Коми: 4 (нёль)
polski: 4 (liczba)
português: Quatro
română: 4 (cifră)
Runa Simi: Tawa
русский: 4 (число)
ᱥᱟᱱᱛᱟᱲᱤ:
Gagana Samoa: Fa (numera)
Scots: 4 (nummer)
Sesotho sa Leboa: 4 (nomoro)
shqip: Katër (4)
sicilianu: Quattru
Simple English: 4 (number)
slovenčina: 4 (číslo)
slovenščina: 4 (število)
ślůnski: 4 (nůmera)
Soomaaliga: 4 (tiro)
کوردی: ٤ (ژمارە)
Sranantongo: Numro 4
српски / srpski: 4 (број)
srpskohrvatski / српскохрватски: 4 (broj)
suomi: 4 (luku)
svenska: 4 (tal)
Tagalog: 4 (bilang)
தமிழ்: 4 (எண்)
татарча/tatarça: 4 (сан)
తెలుగు: నాలుగు
ไทย: 4
ትግርኛ: ኣርባዕተ
Tshivenda: Ina
Türkçe: 4 (sayı)
Türkmençe: 4 (san)
тыва дыл: 4
ᨅᨔ ᨕᨘᨁᨗ: 4 (nomoro)
українська: 4 (число)
اردو: 4 (عدد)
Vahcuengh: 4
vepsän kel’: 4 (lugu)
Tiếng Việt: 4 (số)
West-Vlams: 4 (getal)
Winaray: 4 (ihap)
Wolof: Ñent

Xitsonga: Mune
ייִדיש: 4 (נומער)
Yorùbá: 4 (nọ́mbà)