38304 has 72 divisors (see below), whose sum is σ = 131040. Its totient is φ = 10368.

The previous prime is 38303. The next prime is 38317. The reversal of 38304 is 40383.

38304 is nontrivially palindromic in base 11.

It is a tau number, because it is divible by the number of its divisors (72).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 14.

It is not an unprimeable number, because it can be changed into a prime (38303) 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, 2007 + ... + 2025.

It is an arithmetic number, because the mean of its divisors is an integer number (1820).

2³⁸³⁰⁴ 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 38304, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (65520).

38304 is an abundant number, since it is smaller than the sum of its proper divisors (92736).

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

38304 is a wasteful number, since it uses less digits than its factorization.

38304 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 42 (or 31 counting only the distinct ones).

The product of its (nonzero) digits is 288, while the sum is 18.

The square root of 38304 is about 195.7140771636. The cubic root of 38304 is about 33.7091687286.

Adding to 38304 its reverse (40383), we get a palindrome (78687).

The spelling of 38304 in words is "thirty-eight thousand, three hundred four".