6  

Cardinal  6 six 
Ordinal  6th sixth 
Numeral system  senary 
Factorization  
Divisors  1, 2, 3, 6 
Roman numeral  VI 
Roman numeral (Unicode)  Ⅵ, ⅵ 
Arabic  ٦,6 
Arabic (Urdu)  ۶ 
Amharic  ፮ 
Bengali  ৬ 
Chinese numeral  六，陆 
Devanāgarī  ६ 
Hebrew  ו (Vav) 
Khmer  ៦ 
Thai  ๖ 
Tamil  ௬ 
prefixes  hexa/hex (from Greek) 
Binary  110 
Octal  6 
Duodecimal  6 
Hexadecimal  6 
6 (six) is the natural number following 5 and preceding 7.
The SI prefix for 1000^{6} is exa (E), and for its reciprocal atto (a).
Contents 
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 the smallest perfect number. As a perfect number, 6 is related to the Mersenne prime 3, since 2^{1}(2^{2}  1) = 6. (The next perfect number is 28.) It is the only even perfect number that is not the sum of successive odd cubes.^{[1]} Being perfect six is the root of the 6aliquot tree, and is itself the aliquot sum of only one number; the square number, 25. Unrelated to 6 being a perfect number, a Golomb ruler of length 6 is a "perfect ruler."^{[2]} Six is a congruent number.
Six is the first discrete biprime (2.3) and the first member of the (2.q) discrete biprime family.
Six is the only number that is both the sum and the product of three consecutive positive numbers.^{[3]}
Six is a unitary perfect number, a harmonic divisor number and a highly composite number. The next highly composite number is 12.
5 and 6 form a RuthAaron pair under either definition.
The smallest nonabelian group is the symmetric group S_{3} which has 3! = 6 elements.
S_{6}, with 720 elements, is the only finite symmetric group which has an outer automorphism. This automorphism allows us to construct a number of exceptional mathematical objects such as the S(5,6,12) Steiner system, the projective plane of order 4 and the HoffmanSingleton graph. A closely related result is the following theorem: 6 is the only natural number n for which there is a construction of n isomorphic objects on an nset A, invariant under all permutations of A, but not naturally in 11 correspondence with the elements of A. This can also be expressed category theoretically: consider the category whose objects are the n element sets and whose arrows are the bijections between the sets. This category has a nontrivial functor to itself only for n=6.
6 similar coins can be arranged around a central coin of the same radius so that each coin makes contact with the central one (and touches both its neighbors without a gap), but seven cannot be so arranged. This makes 6 the answer to the twodimensional kissing number problem. The densest sphere packing of the plane is obtained by extending this pattern to the hexagonal lattice in which each circle touches just six others.
6 is the largest of the four allHarshad numbers.
A sixsided polygon is a hexagon, one of the three polygons capable of tiling the plane. 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).
There are six basic trigonometric functions.
There are six convex regular polytopes in four dimensions.
Six is the fourbit binary complement of number nine:
6 = 0110 9 = 1001
The six exponentials theorem guarantees (given the right conditions on the exponents) the transcendence of at least one of a set of exponentials.
Base  Numeral system  

2  binary  110 
3  ternary  20 
4  quaternary  12 
5  quinary  11 
6  senary  10 
over 6 (decimal, hexadecimal)  6 
In base 10, 6 is a 1automorphic number.
Multiplication  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  50  100  1000  

6  12  18  24  30  36  42  48  54  60  66  72  78  84  90  96  102  108  114  120  126  132  138  144  150  300  600  6000 
Division  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  

6  3  2  1.5  1.2  1  0.75  0.6  0.5  0.4  
0.5  1  1.5  2  2.5 
Exponentiation  1  2  3  4  5  6  7  8  9  10  11  12  13  

6  36  216  1296  7776  46656  279936  1679616  10077696  60466176  362797056  2176782336  13060694016  
1  64  729  4096  15625  46656  117649  262144  531441  1000000  1771561  2985984  4826809 
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 Brahmins of India, who wrote it in one stroke like a cursive lowercase e rotated 90 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.^{[4]}
On the sevensegment displays of calculators and watches, 6 is usually written with six segments. Some historical calculator models use just five segments for the 6, by omitting the top horizontal bar. This glyph variant has not caught on; for calculators that can display results in hexadecimal, a 6 that looks like a 'b' is not practical.
Just as in most modern typefaces, in typefaces with text figures the 6 character usually has an ascender, as, for example, in .
This numeral resembles an inverted 9. To disambiguate the two on objects and documents that can be inverted, the 6 has often been underlined, both in handwriting and on printed labels.
See also 666.
Hexa is Greek for "six". Thus:
The prefix "hexa" also occurs in the systematic name of many chemical compounds, such as "hexamethyl"
Sex is a Latin prefix meaning "six". Thus:
The number six is a natural number that comes after the number five, but before the number seven. Six is also the first perfect number which means that the sum of its factors (1, 2 and 3) are equal to the number itself (6). The next perfect number is 28.
In math, the number six is an even number.koi:6 (квать)
