12

Number
$12$ (twelve) is:


 * $2^2 \times 3$


 * The $1$st of three $2$-digit integers divisible by both the sum and product of its digits:
 * $12 = \left({1 + 2}\right) \times 4 = \left({1 \times 2}\right) \times 6$


 * The number of edges of the regular octahedron and its dual, the cube


 * The smallest abundant number:
 * $1 + 2 + 3 + 4 + 6 = 16 > 12$


 * The $3$rd superfactorial after $1, 2$:
 * $12 = 3\$ = 3! \times 2! \times 1!$


 * The $5$th highly composite number after $1, 2, 4, 6$:
 * $\tau \left({12}\right) = 6$


 * The $8$th highly abundant number after $1, 2, 3, 4, 6, 8, 10$:
 * $\sigma \left({12}\right) = 28$


 * The $5$th superabundant number after $1, 2, 4, 6$, and the smallest which is also abundant:
 * $\dfrac {\sigma \left({12}\right)} {12} = \dfrac {28} {12} = 2 \cdotp \dot 3$


 * The $2$nd semiperfect number after $6$:
 * $12 = 2 + 4 + 6$


 * The $3$rd pentagonal number after $1, 5$:
 * $12 = 1 + 4 + 7 = \dfrac {3 \left({3 \times 3 - 1}\right)} 2$


 * The $5$th generalized pentagonal number after $1, 2, 5, 7$:
 * $12 = \dfrac {3 \left({3 \times 3 - 1}\right)} 2$


 * The $9$th (strictly) positive integer after $1, 2, 3, 4, 6, 7, 9, 10$ which cannot be expressed as the sum of exactly $5$ non-zero squares.


 * The number of distinct pentominoes, up to reflection.


 * The base of the duodecimal number system.


 * The $6$th even number after $2, 4, 6, 8, 10$ which cannot be expressed as the sum of $2$ composite odd numbers.


 * The square of the reverse of $12$ equals the reverse of the square of $12$:
 * $12^2 = 144$
 * $21^2 = 441$


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


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


 * $12 = 3 \times 4$, and $56 = 7 \times 8$

Also see

 * 12 Pentominoes
 * Product of Proper Divisors of 12
 * 12 times Sigma of 12 equals 14 times Sigma of 14
 * 8 Mutually Non-Attacking Queens on Chessboard
 * 12 Knights to Attack or Occupy All Squares on Chessboard
 * Twelve Factorial plus One is divisible by 13 Squared
 * Square of Reversal of Small-Digit Number