51993 has 12 divisors (see below), whose sum is σ = 77220. Its totient is φ = 33696.

The previous prime is 51991. The next prime is 52009. The reversal of 51993 is 39915.

51993 is digitally balanced in base 2 and base 4, because in such bases it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 2 ways, for example, as 36864 + 15129 = 192^2 + 123^2 .

It is not a de Polignac number, because 51993 - 2¹ = 51991 is a prime.

It is not an unprimeable number, because it can be changed into a prime (51991) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 423 + ... + 531.

It is an arithmetic number, because the mean of its divisors is an integer number (6435).

2⁵¹⁹⁹³ is an apocalyptic number.

51993 is a gapful number since it is divisible by the number (53) formed by its first and last digit.

It is an amenable number.

51993 is a deficient number, since it is larger than the sum of its proper divisors (25227).

51993 is a wasteful number, since it uses less digits than its factorization.

51993 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 168 (or 165 counting only the distinct ones).

The product of its digits is 1215, while the sum is 27.

The square root of 51993 is about 228.0197359879. The cubic root of 51993 is about 37.3234366483.

The spelling of 51993 in words is "fifty-one thousand, nine hundred ninety-three".