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24 (twenty-four) is the natural number following 23 and preceding 25.
In mathematics
It is the factorial of 4 and a composite number, its proper divisors being 1, 2, 3, 4, 6, 8 and 12, making it a highly composite number. Subtracting one from each of its divisors (except 1 and 2, but including itself) yields a prime number; 24 is the largest number with this property.
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 semi-meandric number.
In science
In astronomy,
- Messier object M24, a magnitude 11.5 star cloud in the constellation Sagittarius, known among other names as Delle Caustiche and the Sagittarius star cloud.
- The New General Catalogue object (http://www.ngcic.org/) NGC 24, a magnitude 11.6 spiral galaxy in the constellation Sculptor
- The Saros number (http://sunearth.gsfc.nasa.gov/eclipse/SEsaros/SEsaros1-175.html) of the solar eclipse series which began on -2134 April 6 and ended on -854 May 14. The duration of Saros series 24 was 1280.1 years, and it contained 72 solar eclipses.
- The Saros number (http://sunearth.gsfc.nasa.gov/eclipse/LEsaros/LEsaros1-175.html) of the lunar eclipse series which began on -2049 September 6 and ended on -516 March 14. The duration of Saros series 24 was 1532.5 years, and it contained 86 lunar eclipses.
- The 24th moon of Jupiter is Pasiphae.
In other fields
Twenty-four is:
- The number of hours in a day.
- The number of cycles in the Chinese solar year.
- The number of books in the Tanakh.
- Usually the number of teeth in a human child's mouth.
- The number of karats in pure gold.
- 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.
- The total number of 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.
- The designation of US Interstate 24, a freeway that runs from Tennessee to Illinois.
- The number of letters in the Greek alphabet in its classical and modern form.
- 24, the television series.
- The number of points in backgammon.
- When pronounced "two-four", a 24-pack 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.
- Historical years: 24 A.D., 24 B.C., or 1924
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