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6 (number)

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Cardinal	6 six
Ordinal	6th sixth
Numeral system	base 6
Factorization	<math> 2 \cdot 3 <math>
Divisors	2, 3
Roman numeral	VI
Prefixes	hexa- (Greek) sex- (Latin)
Binary	110
Octal	6
Duodecimal	6
Hexadecimal	6

6 (six) is the natural number following 5 and preceding 7. Prefixes for 6 include hexa- (Greek) and sex- (Latin).

Evolution of the glyph

The evolution of our modern glyph for 6 appears rather simple when compared with that for the other numerals. Our modern 6 can be traced back to the Brahmin Indians, who wrote it in one stroke like a cursive lowercase e rotated 45 degrees clockwise. Gradually, the upper part of the stroke (above the central squiggle) became more curved, while the lower part of the stroke (below the central squiggle) became straighter. The Ghubar Arabs dropped the part of the stroke below the squiggle. From there, the European evolution to our modern 6 was very straightforward, aside from a flirtation with a glyph that looked more like an uppercase G.

In mathematics

Six is the second smallest composite number, its proper divisors being 1, 2 and 3. Since six equals the sum of these proper divisors, six is a perfect number. As a perfect number, 6 is related to the Mersenne prime 3, since 2¹(2² - 1) = 6. The next perfect number is 28. Six is also a unitary perfect number, a harmonic divisor number and a highly composite number. The next highly composite number is 12.

The smallest non-abelian group is the symmetric group S₃ which has 3! = 6 elements.

In binary code, six is 110; in ternary code six is 20; in quaternary numeral system code six is 12; in quinary six is 11; in senary six is 10; in septenary code and all codes above (such as octal, decimal and hexadecimal) six is 6. Since it is divisible by the sum of its digits in all these bases, 6 is one of the four all-Harshad numbers.

In Roman numerals six is VI.

A six-sided polygon is a hexagon. Figurate numbers representing hexagons (including six) are called hexagonal numbers. Six is also an octahedral number. It is a triangular number and so is its square (36).

In base 10, 6 is a 1-automorphic number.

In other fields

Six is:

• In cricket, a shot in which the ball clears the boundary (cricket) without bouncing; see Six (cricket).
• In rugby union, the position of blindside flanker.
• The atomic number of carbon.
• The length in years of a standard term of a United States senator.
• The name of the smallest group of Cub Scouts, traditionally consisting of six people and is led by a 'sixer'. Logically speaking, this isn't always the case, particularly in packs with less than 6 Cub Scouts in it.
• The number of cans in a six-pack.
• The number of carbon atoms and carbon-carbon bonds in benzene.
• The number of feet below ground level a coffin is traditionally buried; thus, the phrase "six feet under" means that a person (or thing, or concept) is dead.
• The number of inhabited continents, and the total number of continents if Eurasia (Europe plus Asia) is considered a single continent.
• The number of large geyser fields in the world.
• The number of points on a Star of David.
• The number of primary and secondary colors in the rainbow (not counting indigo).
• The number of similar coins that can be arranged around a central seventh coin of the same kind so that each coin makes contact with the central one and touches both its neighbors without a gap; see also Sphere packing.
• The number of strings on a standard guitar.

In addition:

• Number Six was the main character in the television series The Prisoner.
• "Six Geese a Laying" were given as a present on the sixth day in the popular Christmas carol The Twelve Days of Christmas.
• Les Six were a group of Lost Generation writers.
• One of A. A. Milne's poetry books was entitled Now We Are Six.
• Extra-sensory perception is sometimes called the "sixth sense".
• Bands with the number six in their name include Eve 6 and Sixpence None the Richer.
• The Six dynasties form part of Chinese history.
• The Bionic Six are the heroes of an animated series.
• The Birmingham Six were held in prison for 16 years.
• Six Degrees of Kevin Bacon is a game that can be played with the names of actors and actresses.
• RIASEC is a system that places occupations into six categories.
• 666 is considered the Number of the Beast.
• The year "6" can refer to: A.D. 6, 6 B.C., or 1906.

Hexa is Greek for "six". Thus:

• A hexahedron is a polyhedron with six faces, with a cube being a special case.
• A hexapod is an animal with six legs; this includes all insects.
• Hexameter is a poetic form consisting of six feet per line.

The prefix "hexa-" also occurs in the systematic name of many chemical compounds, such as "hexamethyl".

Sex- is a Latin prefix meaning "six". Thus:

• A group of six musicians is called a sextet.
• Six babies delivered in one birth are sextuplets. The first set of sextuplets of whom all six survived are the Dilley Sexuplets.
• People with sexdactyly have six fingers on each hand.
• The measuring instrument called a sextant got its name because its shape forms one sixth of a whole circle.