| ||||
|---|---|---|---|---|
| Cardinal | two hundred forty | |||
| Ordinal | 240th (two hundred fortieth) | |||
| Factorization | 24 × 3 × 5 | |||
| Divisors | 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240 | |||
| Greek numeral | ΣΜ´ | |||
| Roman numeral | CCXL,ccxl | |||
| Binary | 111100002 | |||
| Ternary | 222203 | |||
| Senary | 10406 | |||
| Octal | 3608 | |||
| Duodecimal | 18012 | |||
| Hexadecimal | F016 | |||
240 (two hundred [and] forty) is thenatural number following239 and preceding241.
240 is apronic number, since it can be expressed as the product of two consecutive integers,15 and16.[1] It is asemiperfect number,[2] equal to the concatenation of two of its proper divisors (24 and 40).[3]
It is also the 12thhighly composite number,[4] with 20 divisors in total, more than any smaller number;[5] and arefactorable number or tau number, since one of its divisors is 20, which divides 240 evenly.[6]
240 is thealiquot sum of only two numbers: 120 and 57121 (or 2392); and is part of the12161-aliquot tree that goes: 120,240, 504, 1056, 1968, 3240, 7650, 14112, 32571, 27333, 12161, 1, 0.
It is the smallest number that can be expressed as a sum of consecutive primes in three different ways:[7]
240 ishighly totient, since it has thirty-one totient answers, more than any previous integer.[8]
It is palindromic in bases 19 (CC19), 23 (AA23), 29 (8829), 39 (6639), 47 (5547) and 59 (4459), while aHarshad number in bases 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15 (and 73 other bases).
240 is thealgebraic polynomial degree of sixteen-cyclelogistic map,[9][10][11]
240 is the number of distinct solutions of theSoma cube puzzle.[12]
There are exactly 240 visible pieces of what would be afour-dimensional version of theRubik's Revenge — aRubik's Cube. A Rubik's Revenge in three dimensions has 56 (64 – 8) visible pieces, which means a Rubik's Revenge in four dimensions has 240 (256 – 16) visible pieces.
240 is the number ofelements in the four-dimensional24-cell (or rectified16-cell): 24cells, 96faces, 96edges, and 24vertices. On the other hand, theomnitruncated 24-cell,runcinated 24-cell, andruncitruncated 24-cell all have 240 cells, while therectified 24-cell andtruncated 24-cell have 240 faces. Theruncinated 5-cell,bitruncated 5-cell, andomnitruncated 5-cell (the latter with 240 edges) all sharepentachoric symmetry, oforder 240; four-dimensionalicosahedral prisms withWeyl group also have order 240. Therectified tesseract has 240 elements as well (24 cells, 88 faces, 96 edges, and 32 vertices).
In five dimensions, therectified 5-orthoplex has 240 cells and edges, while thetruncated 5-orthoplex andcantellated 5-orthoplex respectively have 240 cells and vertices. Theuniform prismatic family is of order 240, where its largest member, theomnitruncated 5-cell prism, contains 240 edges. In the still five-dimensional prismatic group, the600-cell prism contains 240 vertices. Meanwhile, in six dimensions, the6-orthoplex has 240tetrahedral cells, where the6-cube contains 240squares as faces (and abirectified 6-cube 240 vertices), with the6-demicube having 240 edges.
E8 in eight dimensions has 240roots.
| |||||||||
| |||||||||
| |||||||||
| |||||||||
| |||||||||
