280 (number)

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← 279 280 281 →
Cardinal two hundred eighty
Ordinal 280th
(two hundred eightieth)
Factorization 23× 5 × 7
Greek numeral ΣΠ´
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[edit]

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).[disputed ]

280 is a base 10 Harshad number.

In geography[edit]

See also the year 280.

Integers from 281 to 289[edit]

281[edit]

282[edit]

282 = 2·3·47, sphenic number

283[edit]

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

284[edit]

285[edit]

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[edit]

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[edit]

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[edit]

289[edit]

289 = 172, centered octagonal number, Friedman number since (8 + 9)^2 = 289.

References[edit]

  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.