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((Hatnote|This article covers the number 280. For the year, see [[280]].))
((Refimprove|date=May 2016))
((Infobox number
| number = 280
))
'''280''' ('''two hundred [and] eighty''') is the [[natural number]] after [[279 (number)|279]] and before [[281 (number)|281]].

==In mathematics==
The denominator of the eighth [[harmonic number]],<ref>((Cite web|url=https://oeis.org/A002805|title=Sloane's A002805 : Denominators of harmonic numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28))</ref> 280 is an [[octagonal number]].<ref>((Cite web|url=https://oeis.org/A000567|title=Sloane's A000567 : Octagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28))</ref> 280 is the smallest octagonal number that is a half of another octagonal number.

There are 280 plane [[tree (graph theory)|tree]]s 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-inline|reason=This seems to be an error, the number of plane (rooted) trees with ten vertices and the number of handshakes (non-intersecting chords with 18 points around a circle) should both be the ninth Catalan number.  OEIS http://oeis.org/A000108 for the Catalan numbers has both of these ideas listed, 
"Ways of joining 2n points on a circle to form n nonintersecting chords." so 18 points is ninth Catalan #
and "a(n) is the number of ordered rooted trees with n nodes, not including the root." so again, 10 roots is Catalan (9).  And this number is 4862, not 280.|date=September 2013))

==Integers from 281 to 289==
===281===
((Main|281 (number)))

===282===
((main|282 (number)))

===283===
((main|283 (number)))

===284===
((main |284 (number)))

===285===
((main|285 (number)))

===286===
((main |286 (number)))

===287===
((Main|287 (number)))

===288===
((Main|288 (number)))

===289===
((main|289 (number)))

== References ==
((Reflist))
((Integers|2))

((DEFAULTSORT:280 (Number)))
[[Category:Integers]]

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