• 52 can be written using four 4's:

52 has 6 divisors (see below), whose sum is σ = 98. Its totient is φ = 24.

The previous prime is 47. The next prime is 53. The reversal of 52 is 25.

52 = T_{3} + T_{4} + ... +
T_{6}.

52 is nontrivially palindromic in base 3, base 5 and base 12.

52 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

52 is an esthetic number in base 16, because in such base its adjacent digits differ by 1.

It can be written as a sum of positive squares in only one way, i.e., 36 + 16 = 6^2 + 4^2 .

It is a sliding number, since 52 = 2 + 50 and 1/2 + 1/50 = 0.52.

It is the 5-th Bell number.

It is a magnanimous number.

It is an alternating number because its digits alternate between odd and even.

52 is an undulating number in base 5.

52 is a nontrivial repdigit in base 12.

It is a plaindrome in base 6, base 9, base 11, base 12, base 14, base 15 and base 16.

It is a nialpdrome in base 4, base 8, base 10, base 12 and base 13.

It is a zygodrome in base 12.

It is a congruent number.

52 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 3 + ... + 10.

52 is the 4-th decagonal number.

It is an amenable number.

52 is a deficient number, since it is larger than the sum of its proper divisors (46).

52 is a wasteful number, since it uses less digits than its factorization.

52 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 17 (or 15 counting only the distinct ones).

The product of its digits is 10, while the sum is 7.

The square root of 52 is about 7.2111025509. The cubic root of 52 is about 3.7325111568.

Adding to 52 its reverse (25), we get a palindrome (77).

Subtracting from 52 its reverse (25), we obtain a cube (27 = 3^{3}).

The spelling of 52 in words is "fifty-two", and thus it is an aban number, an eban number, and an uban number.

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