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| 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,ccxvi | |||
| Binary | 110110002 | |||
| Ternary | 220003 | |||
| Senary | 10006 | |||
| Octal | 3308 | |||
| Duodecimal | 16012 | |||
| Hexadecimal | D816 | |||
216 (two hundred [and] sixteen) is thenatural number following215 and preceding217. It is acube, and is often calledPlato's number, although it is not certain that this is the number intended byPlato.
216 is thecube 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 forEuler'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 ahighly powerful number: the product of the exponents in itsprime 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 theproper divisors of any other integer, it is anuntouchable number.[4] Although it is not asemiprime, 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 atriangular number or as a triangular number plus aprime 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-elementpermutations whose products generate all the other permutations on four elements.[7] There are also 216 fixedhexominoes, thepolyominoes 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 ofPlato's number, a number described in vague terms byPlato in theRepublic. Other interpretations include3600 and12960000.[9]
There are 216 colors in theweb-safe color palette, acolor cube.[10]
The international calling code forTunisia
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