24

Number
$24$ (twenty-four) is:


 * $2^3 \times 3$


 * $4$ factorial:
 * $24 = 4! = 4 \times 3 \times 2 \times 1$


 * The $6$th trimorphic number after $1, 4, 5, 6, 9$:
 * $24^3 = 13 \, 8 \mathbf {24}$


 * The $2$nd of three $2$-digit integers divisible by both the sum and product of its digits:
 * $24 = \left({2 + 4}\right) \times 4 = \left({2 \times 4}\right) \times 3$


 * The $4$th abundant number after $12, 18, 20$:
 * $1 + 2 + 3 + 4 + 6 + 8 + 12 = 36 > 24$


 * The $6$th highly composite number after $1, 2, 4, 6, 12$:
 * $\tau \left({24}\right) = 8$


 * The $6$th superabundant number after $1, 2, 4, 6, 12$:
 * $\dfrac {\sigma \left({24}\right)} {24} = \dfrac {60} {24} = 2 \cdotp 5$


 * The $5$th semiperfect number after $6, 12, 18, 20$:
 * $24 = 1 + 3 + 8 + 12$


 * Divisible by both the sum and product of its digits:
 * $24 = 4 \times \left({2 + 4}\right) = 3 \times \left({2 \times 4}\right)$


 * The smallest composite number the product of whose proper divisors form its cube:
 * $1 \times 2 \times 3 \times 4 \times 6 \times 8 \times 12 = 24^3$


 * The area of the smallest scalene obtuse triangle with integer sides and area:
 * $24 = \sqrt{16 \left({16 - 4}\right) \left({16 - 13}\right) \left({16 - 15}\right)}$
 * where $16 = \dfrac{4 + 13 + 15} 2$


 * The smallest positive integer which can be partitioned into distinct Fibonacci numbers in $5$ different ways:
 * $24 = 21 + 3 = 21 + 2 + 1 = 13 + 8 + 3 = 13 + 8 + 2 + 1 = 13 + 5 + 3 + 2 + 1$


 * The $14$th after $1, 2, 4, 5, 6, 8, 9, 12, 13, 15, 16, 17, 20$ of the $24$ positive integers which cannot be expressed as the sum of distinct non-pythagorean primes.


 * The $24$th pyramidal number is a square:
 * $1^2 + 2^2 + \cdots + 24^2 = 70^2$


 * The $17$th integer $n$ after $0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 18, 19$ such that $2^n$ contains no zero in its decimal representation:
 * $2^{24} = 16 \, 777 \, 216$


 * The $13$th positive integer which is not the sum of $1$ or more distinct squares:
 * $2, 3, 6, 7, 8, 11, 12, 15, 18, 19, 22, 23, 24, \ldots$


 * The $15$th positive integer after $2, 3, 4, 7, 8, 9, 10, 11, 14, 15, 16, 19, 20, 21$ which cannot be expressed as the sum of distinct pentagonal numbers.

Also see

 * Sum of Squares of Divisors of 24 and 26 are Equal
 * Smallest Scalene Obtuse Triangle with Integer Sides and Area
 * Smallest Positive Integer with 5 Fibonacci Partitions
 * Pythagorean Triangles whose Area equal their Perimeter