12  

Cardinal  twelve 
Ordinal  12th (twelfth) 
Numeral system  duodecimal 
Factorization  
Divisors  1, 2, 3, 4, 6, 12 
Roman numeral  XII 
Binary  1100_{2} 
Octal  14_{8} 
Duodecimal  10_{12} 
Hexadecimal  C_{16} 
Mathematical properties  
φ(12) = 4  τ(12) = 6 
σ(12) = 28  π(12) = 5 
μ(12) = 0  M(12) = 2 
12 (twelve) (pronounced /ˈtwɛlv/ ( listen)) is the natural number following 11 and preceding 13.
The word "twelve" is a native English word that presumably arises from the Germanic compound twalif "twoleave", meaning that two is left after one takes away the base, ten. This compound meaning may have been transparent to speakers of Old English, but the modern form "twelve" is quite translucent. Only the remaining tw hints that twelve and two are related. Etymology (Weekley, Skeat) suggests that "twelve" (similar to "eleven") consists of two parts, the first meaning "two" and the second "leftover", so a literal translation would yield "two remaining [after having ten taken]".
A group of twelve things is called a Duodecad. The ordinal adjective is duodenary, twelfth. The adjective referring to a group consisting of twelve things is duodecuple.
The number twelve is often used as a sales unit in trade, and is often referred to as a dozen. Twelve dozen are known as a gross. (Note that there are thirteen items in a baker's dozen.)
As shown below, the number twelve is frequently cited in the Abrahamic religions and is also central to Western calendar and units of time.
Contents 
Twelve is a composite number, the smallest number with exactly six divisors, its proper divisors being 1, 2, 3, 4, and 6. Twelve is also a highly composite number, the next one being 24. It is the first composite number of the form p^{2}q; a squareprime, and also the first member of the (p^{2}) family in this form. 12 has an aliquot sum of 16 (133% in abundance). Accordingly, 12 is the first abundant number (in fact a superabundant number) and demonstrates an 8 member aliquot sequence; {12,16,15,9,4,3,1,0} 12 is the 3rd composite number in the 3aliquot tree. The only number which has 12 as its aliquot sum is the square 121. Only 2 other square primes are abundant (18 and 20).
Twelve is a sublime number, a number that has a perfect number of divisors, and the sum of its divisors is also a perfect number. Since there is a subset of 12's proper divisors that add up to 12 (all of them but with 4 excluded), 12 is a semiperfect number.
If an odd perfect number is of the form 12k + 1, it has at least twelve distinct prime factors.
Twelve is a superfactorial, being the product of the first three factorials. Twelve being the product of three and four, the first four positive integers show up in the equation 12 = 3 × 4, which can be continued with the equation 56 = 7 × 8.
Twelve is the ninth Perrin number, preceded in the sequence by 5, 7, 10, and also appears in the Padovan sequence, preceded by the terms 5, 7, 9 (it is the sum of the first two of these). It is the fourth Pell number, preceded in the sequence by 2 and 5 (it is the sum of the former plus twice the latter).
A twelvesided polygon is a dodecagon. A twelvefaced polyhedron is a dodecahedron. Regular cubes and octahedrons both have 12 edges, while regular icosahedrons have 12 vertices. Twelve is a pentagonal number. The densest threedimensional lattice sphere packing has each sphere touching 12 others, and this is almost certainly true for any arrangement of spheres (the Kepler conjecture). Twelve is also the kissing number in three dimensions.
Twelve is the smallest weight for which a cusp form exists. This cusp form is the discriminant Δ(q) whose Fourier coefficients are given by the Ramanujan τfunction and which is (up to a constant multiplier) the 24th power of the Dedekind eta function. This fact is related to a constellation of interesting appearances of the number twelve in mathematics ranging from the value of the Riemann zeta function function at 1 i.e. ζ(1)=1/12, the fact that the abelianization of SL(2,Z) has twelve elements, and even the properties of lattice polygons.
There are twelve Jacobian elliptic functions and twelve cubic distancetransitive graphs.
The duodecimal system (12_{10} [twelve] = 10_{12}), which is the use of 12 as a division factor for many ancient and medieval weights and measures, including hours, probably originates from Mesopotamia.
In base thirteen and higher bases (such as hexadecimal), twelve is represented as C. In base 10, the number 12 is a Harshad number.
Multiplication  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  25  50  100  1000  

12  24  36  48  60  72  84  96  108  120  132  144  156  168  180  192  204  216  228  240  252  264  300  600  1200  12000 
١٢  Arabic  ԺԲ  Armenian  

ιβʹ  Ionian Greek  ΔΙΙ  Attic Greek  
יב  Hebrew 

Egyptian  
१२  Indian (Devanāgarī)  十二  Chinese and Japanese  
௧௨  Tamil  Ⅻ  Roman and Etruscan  
๑๒  Thai  IIX  Chuvash 
The number 12 is very important in many religions, mainly Judaism and Christianity, but some uses are to be found in pagan times.
In Antiquity there are numerous magical/religious uses of twelves.^{[1]} Ancient Greek religion, the Twelve Olympians were the principal gods of the pantheon. The chief Norse god, Odin, had 12 sons. Several sets of twelve cities are identified in history as a dodecapolis, the most familiar being the Etruscan League. In the King Arthur Legend, Arthur is said to have subdued 12 rebel princes and to have won 12 great battles against Saxon invaders. [source: Benet's Reader's Encyclopedia, 3d ed]
The importance of 12 in Judaism and Christianity can be found in the Bible. The biblical Jacob had 12 sons, who were the progenitors of the Twelve Tribes of Israel, while the New Testament describes twelve apostles of Jesus; when Judas Iscariot was disgraced, a meeting was held (Acts) to add Matthias to complete the number twelve once more. (Today, The Church of Jesus Christ of Latterday Saints has a Quorum of the Twelve Apostles.)
The Book of Revelation contains much numerical symbolism, and a lot of the numbers mentioned have 12 as a divisor. 12:1 mentions a woman — interpreted as the people of Israel, the Church or the Virgin Mary — wearing a crown of twelve stars (representing each of the twelve tribes of Israel). Furthermore, there are 12,000 people sealed from each of the twelve tribes of Israel, making a total of 144,000 (which is the square of 12 multiplied by a thousand).
There are 12 days of Christmas. The song Twelve Days of Christmas came from the traditional practice of extending Yuletide celebrations over the twelve days from Christmas day to the eve of Epiphany; the period of thirteen days including Epiphany is sometimes known as Christmastide. Thus Twelfth Night is another name for the twelfth day of Christmas or January 5 (the eve of Epiphany). Similarly, Eastern Orthodoxy observes 12 Great Feasts.
In Judaism, 12 signifies the age a girl matures (bat mitzvah).
In Shi'a Islam, there are twelve Imams, legitimate successors of the prophet Muhammad. These twelve early leaders of Islam are—Ali, Hasan, Husayn, and nine of Husayn's descendants.
In Hinduism, the sun god Surya has 12 names.
In rugby union one of the centres, most often but not always the inside centre, wears the 12 shirt, while in rugby league, one of the secondrow forwards wears the number 12 jersey.
In both soccer and American Football, the number 12 can be a symbolic reference to the fans because of the support they give to the 11 players on the field. Texas A&M University reserves the number 12 jersey for a walk on player who represents the original "12th Man", a fan who was asked to play when the team's reserves were low in a college American football game in 1922. Similarly, Bayern Munich, Hammarby, Feyenoord, Atlético Mineiro, Flamengo and the Seattle Seahawks do not allow field players to wear the number 12 on their jersey because it is reserved for their supporters.
In the Canadian Football League (CFL) 12 is the maximum number of players that can be on the field of play for each team at any time.
Movies with the number twelve or its variations in their titles include
12 A.D., 12 B.C., 1912, 2012, etc.
Twelve is a number. It comes between eleven and thirteen, and is an even number. It is divisble by 2, 3, 4, and 6. Its ordinal is 12th (twelfth). Its Roman numeral is XII. It is a duodecimal number. Twelve is also the number of monkeys in a Bruce Willis movie.
