38688 has 48 divisors (see below), whose sum is σ = 112896. Its totient is φ = 11520.

The previous prime is 38677. The next prime is 38693. The reversal of 38688 is 88683.

It is a tau number, because it is divible by the number of its divisors (48).

It is a super-2 number, since 2×38688² = 2993522688, which contains 22 as substring.

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

It is a nialpdrome in base 16.

It is a congruent number.

It is an unprimeable number.

38688 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1233 + ... + 1263.

It is an arithmetic number, because the mean of its divisors is an integer number (2352).

2³⁸⁶⁸⁸ 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 38688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (56448).

38688 is an abundant number, since it is smaller than the sum of its proper divisors (74208).

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

38688 is a wasteful number, since it uses less digits than its factorization.

38688 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 57 (or 49 counting only the distinct ones).

The product of its digits is 9216, while the sum is 33.

The square root of 38688 is about 196.6926536503. The cubic root of 38688 is about 33.8214398946.

It can be divided in two parts, 386 and 88, that added together give a palindrome (474).

The spelling of 38688 in words is "thirty-eight thousand, six hundred eighty-eight".