6

Six is the natural number after five and before seven. It is an even composite with prime factorization 2 × 3, and its divisors are 1, 2, 3, and 6. It is the smallest perfect number, since 1 + 2 + 3 = 6. It also equals 3!, the factorial of 3. A regular hexagon has six sides, and a cube has six faces; in group theory the symmetric group on three elements has order six.

Six can be represented in various bases: base-10 as 6, base-2 as 110, base-3 as 20, and base-6 as 10. It is the third triangular number, T3 = 6, and occurs in many combinatorial counts, such as the number of permutations of three items.

In science, carbon has atomic number six, a central element in organic chemistry. Carbon’s tetravalence enables vast molecular diversity. Hexagonal crystal structures occur in graphite and many minerals, and hexagonal close packing describes efficient packing in solids.

Culturally, June is the sixth month in the Gregorian calendar. The number six is often associated with balance; in Chinese culture it is regarded as lucky due to a phonetic resemblance to a word meaning smooth progression. In cricket, a six denotes hitting the ball beyond the boundary for six runs.

Six also features in geometry and design: a regular hexagon tiles the plane in honeycomb patterns, and dice commonly have six faces. Across mathematics, science, and culture, six functions as a foundational count.