240 (number)

From Wikipedia, the free encyclopedia
← 239 240 241 →
List of numbers — Integers
← 0 100 200 300 400 500 600 700 800 900 →
Cardinaltwo hundred forty
Ordinal240th
(two hundred fortieth)
Factorization24 × 3 × 5
Greek numeralΣΜ´
Roman numeralCCXL
Binary111100002
Ternary222203
Octal3608
Duodecimal18012
HexadecimalF016

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.
  • a refactorable number or tau number, since it has 20 divisors and 20 divides 240.
  • a highly totient number, since it has 31 totient answers, more than any previous integer.
  • a pronic number since it can be expressed as the product of two consecutive integers, 15 and 16.
  • palindromic in bases 19 (CC19), 23 (AA23), 29 (8829), 39 (6639), 47 (5547) and 59 (4459).
  • 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. [3]

E8 has 240 roots.

There are 240 distinct solutions of the Soma cube puzzle.[4]

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

References[]

  1. ^ "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-09-05.
  2. ^ "Sloane's A050480 : Numbers that can be written as a concatenation of distinct proper divisors". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-09-05.
  3. ^ "A067373". OEIS. 2009-08-15. Retrieved 2021-08-27.
  4. ^ Weisstein, Eric W. "Soma Cube". Wolfram MathWorld. Retrieved 2016-09-05.
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