# 252 (number)

 ← 251 252 253 →
Cardinal two hundred fifty-two
Ordinal 252nd
(two hundred and 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
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 four pieces on a Connect Four board.[11]

## References

1. ^ "Sloane's A000984 : Central binomial coefficients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ "Sloane's A000594 : Ramanujan's tau function". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. ^
4. ^ "Sloane's A005153 : Practical numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
5. ^ "Sloane's A033950 : Refactorable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-04-18. Retrieved 2016-04-18.
6. ^
7. ^ "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-04-19. Retrieved 2016-04-19.
8. ^
9. ^
10. ^
11. ^