3993 has 8 divisors (see below), whose sum is σ = 5856. Its totient is φ = 2420.

The previous prime is 3989. The next prime is 4001.

3993 is nontrivially palindromic in base 10.

It is an ABA number since it can be written as A⋅B^A, here for A=3, B=11.

It is not a de Polignac number, because 3993 - 2² = 3989 is a prime.

3993 is a Rhonda number in base 12.

It is a plaindrome in base 12.

It is a nialpdrome in base 8, base 11 and base 16.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 3993.

It is not an unprimeable number, because it can be changed into a prime (3923) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 358 + ... + 368.

It is an arithmetic number, because the mean of its divisors is an integer number (732).

2³⁹⁹³ is an apocalyptic number.

3993 is a gapful number since it is divisible by the number (33) formed by its first and last digit.

It is an amenable number.

3993 is a deficient number, since it is larger than the sum of its proper divisors (1863).

3993 is an equidigital number, since it uses as much as digits as its factorization.

3993 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 36 (or 14 counting only the distinct ones).

The product of its digits is 729, while the sum is 24.

The square root of 3993 is about 63.1901891119. The cubic root of 3993 is about 15.8647452734.

Subtracting from 3993 its sum of digits (24), we obtain a square (3969 = 63²).

The spelling of 3993 in words is "three thousand, nine hundred ninety-three".