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252 (number)

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252
  
253 →

Factorization
  
2× 3× 7

Cardinal
  
two hundred fifty-two

Roman numeral
  
CCLII

Ordinal
  
252nd (two hundred and fifty-second)

Divisors
  
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252

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

In mathematics

252 is:

  • the central binomial coefficient ( 10 5 ) , the largest one divisible by all coefficients in the previous line
  • a Harshad number in base 10.
  • τ ( 3 ) , where τ is the Ramanujan tau function.
  • σ 3 ( 6 ) , where σ 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.
  • 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 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, and 252 ways of placing four pieces on a Connect Four board.

    References

    252 (number) Wikipedia
    (Text) CC BY-SA