252 (number)

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

← 251 252 253 →
← 250 251 252 253 254 255 256 257 258 259 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	two hundred fifty-two
Ordinal	252nd (two hundred fifty-second)
Factorization	22 × 32 × 7
Divisors	1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
Greek numeral	ΣΝΒ´
Roman numeral	CCLII, cclii
Binary	111111002
Ternary	1001003
Senary	11006
Octal	3748
Duodecimal	19012
Hexadecimal	FC16

In mathematics

252 is:

• the central binomial coefficient ${\displaystyle {\tbinom {10}{5}}}$, the largest one divisible by all coefficients in the previous line^[1]
• ${\displaystyle \tau (3)}$, where ${\displaystyle \tau }$ is the Ramanujan tau function.^[2]
• ${\displaystyle \sigma _{3}(6)}$, where ${\displaystyle \sigma _{3}}$ is the function that sums the cubes of the divisors of its argument:^[3]

${\displaystyle 1^{3}+2^{3}+3^{3}+6^{3}=(1^{3}+2^{3})(1^{3}+3^{3})=252.}$

• a practical number,^[4]
• a refactorable number,^[5]
• a hexagonal pyramidal number.^[6]
• a member of the Mian-Chowla sequence.^[7]

There are 252 points on the surface of a cuboctahedron of radius five in the face-centered cubic lattice,^[8] 252 ways of writing the number 4 as a sum of six squares of integers,^[9] 252 ways of choosing four squares from a 4×4 chessboard up to reflections and rotations,^[10] and 252 ways of placing three pieces on a Connect Four board.^[11]