24 is a natural number that comes after twenty-three and before twenty-five. It is an even number and a composite integer with a small set of familiar divisors. In elementary contexts 24 often appears in counting problems, timekeeping, and measures of purity such as carats.
Mathematical properties
The prime factorization of 24 is 2^3 × 3. That structure gives 24 eight positive divisors. It equals 4! (4 factorial), so it represents the number of permutations of four distinct objects. Many algebraic and combinatorial identities feature 24 because of these simple factors.
- Divisors: 1, 2, 3, 4, 6, 8, 12, 24
- Number of divisors: 8
- Sum of all divisors: 60; sum of proper divisors: 36 (so 24 is an abundant number)
- Factorial: 4! = 24
History and cultural uses
Across cultures and technologies, 24 appears frequently. Most notably, many timekeeping systems divide the day into 24 hours, a convention long established in astronomy and civil timekeeping. Jewelry often refers to 24-carat gold as pure gold, and in Western music there are 24 major and minor keys (12 of each) in standard equal temperament.
Examples and applications
In geometry and symmetry, 24 is the order of the rotational symmetry group of a cube or an octahedron, and it is also the order of the symmetric group S4, the set of permutations of four elements. In chemistry, the atomic number 24 identifies the element chromium. In popular media the title 24 (television series) became well known in the United States and internationally, which has reinforced the number's visibility in modern culture.
Notable distinctions
Because 24 has more divisors than any smaller positive integer, it is classified as a highly composite number. Its combination of small prime factors makes it versatile in measurements, tilings, group orders and combinatorial counts, so it recurs across mathematics, science, technology and everyday life.