24 (
twentyfour) is the
natural number following
23 and preceding
25.
The
SI prefix for 10
^{24} is
yotta (Y), and for 10
^{24} (i.e., the
reciprocal of 10
^{24})
yocto (y).
These numbers are the largest and smallest number to receive an SI
prefix to date.
In mathematics
 24 is the factorial of 4 and a
composite number, being the first
number of the form 2^3q, where q is an odd
prime.
 It is the smallest number with exactly eight divisors: 1, 2, 3, 4, 6, 8, 12, and 24. It is a
highly composite number,
having more divisors than any smaller number. Adding up all the
proper divisors of 24 except 4 and 8 gives 24, hence 24 is a
semiperfect number.
 Subtracting one from any of its divisors (except 1 and 2, but
including itself) yields a prime
number. 24 is the largest number with this property, for to
have this property a number cannot be divisible by a prime greater
than three, nor can it be divisible by 9 or 16.
 24 has an aliquot sum of 36 and the
aliquot sequence (24,36,55,17,1,0).
Twentyfour is only the aliquot sum of
one number the square 529.
 There are 10 solutions to the equation φ(x) = 24, namely 35, 39,
45, 52, 56, 70, 72, 78, 84 and 90. This is more than any integer
below 24, making 24 a highly
totient number.
 24 is a nonagonal number. This
number is also the sum of a twin prime
(11 + 13). It is a Harshad number and
a semimeandric number.
 Together with the number one, 24 is one of the few numbers n
for which the sum of \mu(d)d^2 over the divisors d of n is equal to
itself.
 The product of any four consecutive numbers is divisible by 24.
This is because, among any four consecutive numbers, there must be
two even numbers, one of which is a multiple of four, and there
must be a multiple of three.
 In 24 dimensions there are 24 even positive definite unimodular lattices, called the Niemeier lattices. One of these is the
exceptional Leech lattice which has
many surprising properties; due to its existence, the answers to
many problems such as the kissing
number problem and sphere packing
are known in 24 dimensions but not in many lower dimensions. The
Leech lattice is closely related to the equally nice length24
binary Golay code and the Steiner system S(5,8,24) and the Mathieu group M_{24}. One construction
of the Leech lattice is possible
because of the remarkable fact that
1^{2}+2^{2}+3^{2}+...+24^{2}
=70^{2} is a perfect square;
24 is the only integer greater than 1 with this property. These
properties of 24 are related to the fact that the number 24 also
appears in several places in the theory of modular forms; for example, the modular discriminant is the 24th power
of the Dedekind eta
function.
 The BarnesWall lattice
contains 24 lattice.
 24 is the highest number n with the property that
every element of the group of units
^{*} of
the commutative ring Z/nZ',
apart from the identity element, has order 2; thus the
multiplicative group
(Z/24Z)^{*} =
{1,5,7,11,13,17,19,23} is isomorphic to the additive group
(Z/2Z)^{3}. This fact plays a role in
monstrous moonshine.
 The 24cell, with 24 octahedral cells
and 24 vertices, is a selfdual
convex regular 4polytope;
it has no good 3dimensional analogue.
 For any prime p greater than 3, p^21 is divisible by 24 with
no remainder.
In science
In religion
In music
 There are 24 major and minor keys in Western tonal music, not counting enharmonic equivalents. Therefore, for
collections of pieces written in each key, the number of pieces in
such a collection; e.g., Chopin's 24 Preludes
In sports
 The current jersey number of NBA star, Kobe Bryant (from the 200607 season,
onwards)
 The jersey number of NFL Stars, Champ
Bailey,Michael Huff,Deltha O'neal,Ty
Law,Charles Woodson,Cadillac Williams, and Marion Barber
 The number of teams that participated in each FIFA World Cup finals tournament between 1982
and 1994.
 The retired jersey number of Boston Bruins hockey joueur,
Terry O'Reilly
 The jersey number of NHL Hall of Famer Bernie Federko, retired by the St. Louis Blues
 The
number of accepted runners in the Melbourne Cup
 The number of Stanley Cups won by
the Montreal Canadiens of the
NHL.
In other fields
Astronomical clock in Prague
24 is also:
 The number of bits a computer needs to
represent truecolour images (for a
maximum of 16,777,216 colours). (But greater numbers of bits
provide more accurate colors. "Truecolor" is one of many possible
color representations.)
 The number of a broadcast
television channel
 The number of Carat representing
100% pure gold.
 The number of cycles in the Chinese
solar year.
 The number of frames per second at which motion picture
film is usually projected.
 The number of hours in a day.
 The number of letters in both the modern and classical Greek alphabet. For the latter reason, also
the number of chapters or "books" into which Homer's Odyssey and
Iliad came to be divided.

 24, television series
starring Kiefer Sutherland. Each
episode covers one hour, with 24 episodes making up one entire
"day".
 The number of points on a backgammon
board.
 When pronounced "twofour", a 24pack of beer (Canadianism).
 A children's mathematical game involving the use of any of the
4 standard operations on 4 numbers on a card to get 24 (see
Math 24)
 "24", a song by Welsh musician Jem
 The maximum number of Knight Companions in the Order of the Garter
 The Twentyfourth
Amendment to the United States Constitution is one of the
Civil
Rightsera amendments, abolishing poll tax requirements in
federal elections.
 The
designation of US Interstate 24, a
freeway that runs from Tennessee to Illinois. Also
many other roads called Route 24
 24 is considered an unlucky number in Cantonese culture because
its pronunciation is similar to that of "easy to die". For this
reason, many buildings skip this floor number. The same goes for
13, 34, 44, etc.
 #24 is a recurring
character on The Venture
Bros.
 A Straight Edge symbol, for X is
the 24th letter of the alphabet.
 The
number of the French department Dordogne.
 In
Brazil the number is associated with homosexuals due to the number representing the
deer in the gambling game Jogo do Bicho and the word viado (a
misspelling of veado, deer in Portuguese) being a slang for
homosexuals.
Historical years
24 A.D.,
24
B.C.,
1924,
2024,
etc.
References
 Neil Sloane,
" A046970 formatted as a simple table" The only
times n = a(n) are for n = 1,
24. The table only goes up to 60, though.
External links