280 (number)

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

← 279 280 281 →
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Cardinaltwo hundred eighty
Ordinal280th
(two hundred eightieth)
Factorization23 × 5 × 7
Greek numeralΣΠ´
Roman numeralCCLXXX
Binary1000110002
Ternary1011013
Octal4308
Duodecimal1B412
Hexadecimal11816

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

See also the year 280.

Integers from 281 to 289

281
Main article: 281 (number)

282

282 = 2·3·47, sphenic number

283

283 prime, twin prime with 281, strictly non-palindromic number

284
Main article: 284 (number)

285

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

286 = 2·11·13, sphenic number, tetrahedral number, nontotient, also shorthand for the Intel 80286 microprocessor chip.

286 is the smallest even pseudoprime (not divisible by 3) to base 3, which implies 3285 ≡ 1 (mod 286).

287

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
Main article: 288 (number)

289

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.
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