# 252 (number)

 ← 251 252 253 →
Cardinaltwo hundred fifty-two
Ordinal252nd
(two hundred fifty-second)
Factorization22 × 32 × 7
Divisors1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
Greek numeralΣΝΒ´
Roman numeralCCLII
Binary111111002
Ternary1001003
Octal3748
Duodecimal19012

252 (two hundred [and] fifty-two) is the natural number following 251 and preceding 253.

## In mathematics

252 is:

• the central binomial coefficient ${\tbinom {10}{5}}$ , the largest one divisible by all coefficients in the previous line
• a Harshad number in base 10.
• $\tau (3)$ , where $\tau$ is the Ramanujan tau function.
• $\sigma _{3}(6)$ , where $\sigma _{3}$ is the function that sums the cubes of the divisors of its argument:
$1^{3}+2^{3}+3^{3}+6^{3}=(1^{3}+2^{3})(1^{3}+3^{3})=252.$ There are 252 points on the surface of a cuboctahedron of radius five in the face-centered cubic lattice, 252 ways of writing the number 4 as a sum of six squares of integers, 252 ways of choosing four squares from a 4×4 chessboard up to reflections and rotations, and 252 ways of placing three pieces on a Connect Four board.