52 (fifty-two) is the natural number following 51 and preceding 53.

In mathematics

Fifty-two is

  • a composite number; a square-prime, of the form p2 · q , where q is some prime larger than p . It is the sixth of this form and the fifth of the form 22 · q .
  • the 5th Bell number, the number of ways to partition a set of 5 objects.
  • a decagonal number.
  • with an aliquot sum of 46; within an aliquot sequence of seven composite numbers { 52, 46, 26, 16, 15, 9, 4, 3, 1, 0 } to the prime in the 3-aliquot tree. This sequence does not extend above 52 because it is,
  • an untouchable number, since it is never the sum of proper divisors of any number. It is the first untouchable number larger than 2 and 5.
  • a noncototient since it is not equal to x − φ(x) for any x .
  • a vertically symmetrical number, (as on calculator displays).

In other fields

A full-size piano has 52 white keys, out of 88 total keys.

Fifty-two is:

  • The number of cards in a standard deck of playing cards, not counting Jokers or advertisement cards
  • The number of weeks in a calendar year
  • The number of white keys on a piano
  • The number of explicit bits used to store the significand in an IEEE 754 double