33864 has 32 divisors (see below), whose sum is σ = 90720. Its totient is φ = 10496.

The previous prime is 33863. The next prime is 33871. The reversal of 33864 is 46833.

33864 is nontrivially palindromic in base 16.

It is a super-2 number, since 2×33864² = 2293540992, which contains 22 as substring.

It is a hoax number, since the sum of its digits (24) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a nude number because it is divisible by every one of its digits.

It is a d-powerful number, because it can be written as 3² + 3³ + 8⁵ + 6² + 4⁵ .

It is not an unprimeable number, because it can be changed into a prime (33863) 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, 367 + ... + 449.

It is an arithmetic number, because the mean of its divisors is an integer number (2835).

2³³⁸⁶⁴ is an apocalyptic number.

33864 is a gapful number since it is divisible by the number (34) 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 33864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (45360).

33864 is an abundant number, since it is smaller than the sum of its proper divisors (56856).

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

33864 is a wasteful number, since it uses less digits than its factorization.

33864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 109 (or 105 counting only the distinct ones).

The product of its digits is 1728, while the sum is 24.

The square root of 33864 is about 184.0217378464. The cubic root of 33864 is about 32.3528654673.

The spelling of 33864 in words is "thirty-three thousand, eight hundred sixty-four".