240 (number)

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← 239 240 241 →
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
Binary 111100002
Ternary 222203
Senary 10406
Octal 3608
Duodecimal 18012
Hexadecimal F016

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

Mathematics

240 is a pronic number, since it can be expressed as the product of two consecutive integers, 15 and 16. [1] It is a semiperfect number, [2] equal to the concatenation of two of its proper divisors (24 and 40). [3]

It is also a highly composite number with 20 divisors in total, more than any smaller number; [4] and a refactorable number or tau number, since one of its divisors is 20, which divides 240 evenly. [5]

240 is the aliquot sum of only two numbers: 120 and 57121 (or 2392); and is part of the 12161-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: [6]

240 is highly totient, since it has thirty-one totient answers, more than any previous integer. [7]

It is palindromic in bases 19 (CC19), 23 (AA23), 29 (8829), 39 (6639), 47 (5547) and 59 (4459), while a Harshad number in bases 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15 (and 73 other bases).

240 is the algebraic polynomial degree of sixteen-cycle logistic map, [8] [9] [10]

240 is the number of distinct solutions of the Soma cube puzzle. [11]

There are exactly 240 visible pieces of what would be a four-dimensional version of the Rubik's Revenge — a Rubik'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.

E8 has 240 roots.

Related Research Articles

90 (ninety) is the natural number following 89 and preceding 91.

24 (twenty-four) is the natural number following 23 and preceding 25.

72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or 6 dozen.

34 (thirty-four) is the natural number following 33 and preceding 35.

36 (thirty-six) is the natural number following 35 and preceding 37.

58 (fifty-eight) is the natural number following 57 and preceding 59.

64 (sixty-four) is the natural number following 63 and preceding 65.

96 (ninety-six) is the natural number following 95 and preceding 97. It is a number that appears the same when turned upside down.

104 is the natural number following 103 and preceding 105.

100 or one hundred is the natural number following 99 and preceding 101.

300 is the natural number following 299 and preceding 301.

<span class="mw-page-title-main">360 (number)</span> Natural number

360 is the natural number following 359 and preceding 361.

180 is the natural number following 179 and preceding 181.

500 is the natural number following 499 and preceding 501.

800 is the natural number following 799 and preceding 801.

135 is the natural number following 134 and preceding 136.

225 is the natural number following 224 and preceding 226.

1728 is the natural number following 1727 and preceding 1729. It is a dozen gross, or one great gross. It is also the number of cubic inches in a cubic foot.

744 is the natural number following 743 and preceding 745.

888 is the natural number following 887 and preceding 889.

References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA002378(Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-30.
  2. ↑ "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-09-05.
  3. ↑ "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.
  4. ↑ "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA033950(Refactorable numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-04-18.
  6. ↑ "Sloane's A067373 : Integers expressible as the sum of (at least two) consecutive primes in at least 3 ways". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2009-08-15. Retrieved 2021-08-27.
  7. ↑ "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  8. ↑ Bailey, D. H.; Borwein, J. M.; Kapoor, V.; Weisstein, E. W. (2006). "Ten Problems in Experimental Mathematics" (PDF). American Mathematical Monthly . 113 (6). Taylor & Francis: 482–485. doi:10.2307/27641975. JSTOR   27641975. MR   2231135. S2CID   13560576. Zbl   1153.65301 – via JSTOR.
  9. ↑ Sloane, N. J. A. (ed.). "SequenceA091517(Decimal expansion of the value of r corresponding to the onset of the period 16-cycle in the logistic map.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-29.
  10. ↑ Sloane, N. J. A. (ed.). "SequenceA118454(Algebraic degree of the onset of the logistic map n-bifurcation.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-29.
  11. ↑ Weisstein, Eric W. "Soma Cube". Wolfram MathWorld. Retrieved 2016-09-05.
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