# 240 (number)

From HandWiki

__: Natural number__

**Short description**
| ||||
---|---|---|---|---|

Cardinal | two hundred forty | |||

Ordinal | 240th (two hundred fortieth) | |||

Factorization | 2^{4} × 3 × 5 | |||

Greek numeral | ΣΜ´ | |||

Roman numeral | CCXL | |||

Binary | 11110000_{2} | |||

Ternary | 22220_{3} | |||

Quaternary | 3300_{4} | |||

Quinary | 1430_{5} | |||

Senary | 1040_{6} | |||

Octal | 360_{8} | |||

Duodecimal | 180_{12} | |||

Hexadecimal | F0_{16} | |||

Vigesimal | C0_{20} | |||

Base 36 | 6O_{36} |

**240** (**two hundred [and] forty**) is the natural number following 239 and preceding 241.

## In mathematics

**240** is:

- a semiperfect number.
^{[1]} - a concatenation of two of its proper divisors.
^{[2]} - a highly composite number since it has 20 divisors total (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240), more than any previous number.
^{[3]} - a refactorable number or tau number, since it has 20 divisors and 20 divides 240.
^{[4]} - a highly totient number, since it has 31 totient answers, more than any previous integer.
^{[5]} - a pronic number since it can be expressed as the product of two consecutive integers, 15 and 16.
^{[6]} - palindromic in bases 19 (CC
_{19}), 23 (AA_{23}), 29 (88_{29}), 39 (66_{39}), 47 (55_{47}) and 59 (44_{59}). - a Harshad number in bases 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15 (and 73 other bases).
- the aliquot sum of 120 and 57121.
- part of the 12161-aliquot tree. The aliquot sequence starting at 120 is: 120,
**240**, 504, 1056, 1968, 3240, 7650, 14112, 32571, 27333, 12161, 1, 0.

240 is the smallest number that can be expressed as a sum of consecutive primes in three different ways: 240 = 113 + 127 = 53 + 59 + 61 + 67 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43. ^{[7]}

There are 240 distinct solutions of the Soma cube puzzle.^{[8]}

## In other fields

240 is:

- A common voltage in the
*United Kingdom*and*Australia*before conversion to 230 V standard. - In pre-decimal British currency, the number of pence in a pound until 1971.
- A cholesterol level of 240 and above is considered high risk.
- The model number of the Convair 240.
- The year A.D. 240 or 240 BC.
- Datsun 240Z
- Mercedes 240D
- Nissan 240SX
- Volvo 240
- An area code overlay of the 301 area code in western Maryland.
- The famous skit by the sketch comedy group The State is entitled "$240 Worth of Pudding"
- .240 Weatherby Magnum, rifle cartridge
- 2-4-0, a Whyte notation classification of steam locomotive
- The top speed, in kilometers per hour, of the fastest roller coaster in the world, Formula Rossa.

## References

- ↑ "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". OEIS Foundation. https://oeis.org/A005835.
- ↑ "Sloane's A050480 : Numbers that can be written as a concatenation of distinct proper divisors". OEIS Foundation. https://oeis.org/A050480.
- ↑ "Sloane's A002182 : Highly composite numbers". OEIS Foundation. https://oeis.org/A002182.
- ↑ Sloane, N. J. A., ed. "Sequence A033950 (Refactorable numbers)". OEIS Foundation. https://oeis.org/A033950. Retrieved 2016-04-18.
- ↑ "Sloane's A097942 : Highly totient numbers". OEIS Foundation. https://oeis.org/A097942.
- ↑ Sloane, N. J. A., ed. "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". OEIS Foundation. https://oeis.org/A002378. Retrieved 2016-05-30.
- ↑ "Sloane's A067373 : Integers expressible as the sum of (at least two) consecutive primes in at least 3 ways". OEIS Foundation. 2009-08-15. https://oeis.org/A067373.
- ↑ Weisstein, Eric W.. "Soma Cube". http://mathworld.wolfram.com/SomaCube.html.

Original source: https://en.wikipedia.org/wiki/240 (number).
Read more |