3864 has 32 divisors (see below), whose sum is σ = 11520. Its totient is φ = 1056.

The previous prime is 3863. The next prime is 3877. The reversal of 3864 is 4683.

3864 = T₂₇ + T₂₈ + ... + T₃₄.

3864 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a Smith number, since the sum of its digits (21) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (21).

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

It is one of the 548 Lynch-Bell numbers.

It is a plaindrome in base 15.

It is a nialpdrome in base 8.

It is a zygodrome in base 2.

It is a self number, because there is not a number n which added to its sum of digits gives 3864.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 3864.

It is not an unprimeable number, because it can be changed into a prime (3863) 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, 157 + ... + 179.

It is an arithmetic number, because the mean of its divisors is an integer number (360).

3864 is a Friedman number, since it can be written as (6^4-8)*3, using all its digits and the basic arithmetic operations.

2³⁸⁶⁴ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 3864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (5760).

3864 is an abundant number, since it is smaller than the sum of its proper divisors (7656).

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

3864 is a wasteful number, since it uses less digits than its factorization.

3864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 39 (or 35 counting only the distinct ones).

The product of its digits is 576, while the sum is 21.

The square root of 3864 is about 62.1610810717. The cubic root of 3864 is about 15.6920267302.

The spelling of 3864 in words is "three thousand, eight hundred sixty-four".