38208 has 28 divisors (see below), whose sum is σ = 101600. Its totient is φ = 12672.

The previous prime is 38201. The next prime is 38219. The reversal of 38208 is 80283.

It is a super-3 number, since 3×38208³ = 167333991284736, which contains 333 as substring.

It is a nialpdrome in base 4 and base 16.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (38201) by changing a digit.

38208 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 93 + ... + 291.

2³⁸²⁰⁸ 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 38208, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (50800).

38208 is an abundant number, since it is smaller than the sum of its proper divisors (63392).

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

38208 is a wasteful number, since it uses less digits than its factorization.

38208 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 214 (or 204 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 21.

The square root of 38208 is about 195.4686675659. The cubic root of 38208 is about 33.6809837918.

It can be divided in two parts, 3820 and 8, that added together give a triangular number (3828 = T₈₇).

The spelling of 38208 in words is "thirty-eight thousand, two hundred eight".