280 (number)

← 279 280 281 →
← 200 210 220 230 240 250 260 270 280 290 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	two hundred eighty
Ordinal	280th (two hundred and eightieth)
Factorization	2^3× 5 × 7
Roman numeral	CCLXXX
Binary	1000110002
Ternary	1011013
Quaternary	101204
Quinary	21105
Senary	11446
Octal	4308
Duodecimal	1B412
Hexadecimal	11816
Vigesimal	E020
Base 36	7S36

280 (two hundred [and] eighty) is the natural number after 279 and before 281.

In mathematics

The denominator of the eighth harmonic number,^[1] 280 is an octagonal number.^[2]

There are 280 plane trees with ten nodes. As a consequence of this, 18 people around a round table can shake hands with each other in non-crossing ways, in 280 different ways (this includes rotations).

280 is a base 10 Harshad number.

In geography

• List of highways numbered 280

See also the year 280.

281 to 289

281

Two hundred [and] eighty-one 281 prime, twin prime with 283, Sophie Germain prime, sum of the first fourteen primes, sum of seven consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53), Chen prime, Eisenstein prime with no imaginary part, centered decagonal number

282

Two hundred [and] eighty-two 282 = 2·3·47, sphenic number

283

Two hundred [and] eighty-three 283 prime, twin prime with 281, strictly non-palindromic number

284

Two hundred [and] eighty-four 284= 2·2·71, amicable number with 220; nontotient. 284 degrees Celsius is the flash point of paper.

285

Two hundred [and] eighty-five 285 = 3·5·19, sphenic number, square pyramidal number, Harshad number, also in Star Trek, the total number of Rules of Acquisition, repdigit in base 7 (555).

286

Two hundred [and] eighty-six 286 = 2·11·13, sphenic number, tetrahedral number, nontotient, also shorthand for the Intel 80286 microprocessor chip

287

Two hundred [and] eighty-seven 287 = 7·41, sum of three consecutive primes (89 + 97 + 101), sum of five consecutive primes (47 + 53 + 59 + 61 + 67), sum of nine consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47), Kynea number, pentagonal number, also shorthand for the Intel math coprocessor to the 80286

288

Two hundred [and] eighty-eight 288 = 2⁵·3², is a pentagonal pyramidal number, is 4 superfactorial since 288 = 1!·2!·3!·4!, is an untouchable number, a Harshad number in base 10, a self number, is sum of the sequence of integers 1..4 to the second tetration since 288 = 1 + 4 + 27 + 256 = 1¹ + 2² + 3³ + 4⁴, the number of labelled pointed rooted trees (vertebrates) with up to 4 nodes, the number of maximal directed Pseudoforests on up to 4 vertices, the number of Endofunctions for all sets with <=4 points, and is two dozen sets of a dozen, thus being two gross, often told as a pun in maths classes, the average surface temperature of Earth on the Kelvin temperature scale.

289

Two hundred [and] eighty-nine 289 = 17², centered octagonal number, Friedman number since (8 + 9)^2 = 289.

References

1. "Sloane's A002805 : Denominators of harmonic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
2. "Sloane's A000567 : Octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.