51968 has 36 divisors (see below), whose sum is σ = 122640. Its totient is φ = 21504.

The previous prime is 51949. The next prime is 51971. The reversal of 51968 is 86915.

It is a Harshad number since it is a multiple of its sum of digits (29).

It is an Ulam number.

It is a nialpdrome in base 16.

It is a self number, because there is not a number n which added to its sum of digits gives 51968.

It is an unprimeable number.

51968 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 (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 1778 + ... + 1806.

2⁵¹⁹⁶⁸ is an apocalyptic number.

51968 is a gapful number since it is divisible by the number (58) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 51968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (61320).

51968 is an abundant number, since it is smaller than the sum of its proper divisors (70672).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

51968 is an equidigital number, since it uses as much as digits as its factorization.

51968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 52 (or 38 counting only the distinct ones).

The product of its digits is 2160, while the sum is 29.

The square root of 51968 is about 227.9649095804. The cubic root of 51968 is about 37.3174535639.

The spelling of 51968 in words is "fifty-one thousand, nine hundred sixty-eight".