252 (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, cclii
Binary	111111002
Ternary	1001003
Senary	11006
Octal	3748
Duodecimal	19012
Hexadecimal	FC16

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

In mathematics

252 is:

• a composite number.
• a practical number.
• a hexagonal pyramidal number.
• the central binomial coefficient ${\tbinom {10}{5}}$, the largest one divisible by all coefficients in the previous line.
• a member of the Mian–Chowla sequence.
• a refactorable number.
• palindromic in bases 5 (2002₅), 10 (252₁₀), 17 (EE₁₇), 20 (CC₂₀), 27 (99₂₇), 35 (77₃₅), 41 (66₄₁), 62 (44₆₂) and 3 other bases.
• a Harshad number in bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15 (and 60 other bases).
• $\tau (3)$, 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:

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

• the aliquot sum of 63001.
• part of the 59-aliquot tree. The aliquot sequence starting at 63001 is: 63001, 252, 476, 532, 588, 1008, 2216, 1954, 980, 1414, 1034, 694, 350, 394, 200, 265, 59, 1, 0.

There are:

• 252 points on the surface of a cuboctahedron of radius five in the fcc 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,
• 252 ways of placing four pieces on a Connect Four board.