252 (number)

Short description: Natural number

← 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
Binary	111111002
Ternary	1001003
Quaternary	33304
Quinary	20025
Senary	11006
Octal	3748
Duodecimal	19012
Hexadecimal	FC16
Vigesimal	CC20
Base 36	7036

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

In mathematics

252 is:

• the central binomial coefficient [math]\displaystyle{ \tbinom{10}{5} }[/math], the largest one divisible by all coefficients in the previous line
• [math]\displaystyle{ \tau(3) }[/math], where [math]\displaystyle{ \tau }[/math] is the Ramanujan tau function.
• [math]\displaystyle{ \sigma_3(6) }[/math], where [math]\displaystyle{ \sigma_3 }[/math] is the function that sums the cubes of the divisors of its argument:

[math]\displaystyle{ 1^3+2^3+3^3+6^3=(1^3+2^3)(1^3+3^3)=252. }[/math]

• a practical number,
• a refactorable number,
• a hexagonal pyramidal number.
• a member of the Mian-Chowla sequence.

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.