# 252 (number)

 ← 251 252 253 →
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
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 ${\displaystyle {\tbinom {10}{5}}}$, the largest one divisible by all coefficients in the previous line[1]
• a Harshad number in base 10.
• ${\displaystyle \tau (3)}$, 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]
${\displaystyle 1^{3}+2^{3}+3^{3}+6^{3}=(1^{3}+2^{3})(1^{3}+3^{3})=252.}$

There are 252 points on the surface of a cuboctahedron of radius five in the fcc 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]