216 (two hundred [and] sixteen) is the natural number following 215 and preceding 217. It is a cube, and is often called Plato's number, although it is not certain that this is the number intended by Plato.
| ||||
|---|---|---|---|---|
| Cardinal | two hundred sixteen | |||
| Ordinal | 216th (two hundred sixteenth) | |||
| Factorization | 23 × 33 | |||
| Divisors | 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216 | |||
| Greek numeral | ΣΙϚ´ | |||
| Roman numeral | CCXVI | |||
| Binary | 110110002 | |||
| Ternary | 220003 | |||
| Senary | 10006 | |||
| Octal | 3308 | |||
| Duodecimal | 16012 | |||
| Hexadecimal | D816 | |||
216 is the cube of 6, and the sum of three cubes:
It is the smallest cube that can be represented as a sum of three positive cubes,[1] making it the first nontrivial example for Euler's sum of powers conjecture. It is, moreover, the smallest number that can be represented as a sum of any number of distinct positive cubes in more than one way.[2] It is a highly powerful number: the product 
of the exponents in its prime factorization 
is larger than the product of exponents of any smaller number.[3]
Because there is no way to express it as the sum of the proper divisors of any other integer, it is an untouchable number.[4] Although it is not a semiprime, the three closest numbers on either side of it are, making it the middle number between twin semiprime-triples, the smallest number with this property.[5] Sun Zhiwei has conjectured that each natural number not equal to 216 can be written as either a triangular number or as a triangular number plus a prime number; however, this is not possible for 216. If the conjecture is true, 216 would be the only number for which this is not possible.[6]
There are 216 ordered pairs of four-element permutations whose products generate all the other permutations on four elements.[7] There are also 216 fixed hexominoes, the polyominoes made from 6 squares, joined edge-to-edge. Here "fixed" means that rotations or mirror reflections of hexominoes are considered to be distinct shapes.[8]
216 is one common interpretation of Plato's number, a number described in vague terms by Plato in the Republic. Other interpretations include 3600 and 12960000.[9]
There are 216 colors in the web-safe color palette, a 
In the game of checkers, there are 216 different positions that can be reached by the first three moves.[11]
The proto-Kabbalistic work Sefer Yetzirah states that the creation of the world was achieved by the manipulation of 216 sacred letters.[12]