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:
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 color cube.[10]
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]