38624 has 24 divisors (see below), whose sum is σ = 81648. Its totient is φ = 17920.

The previous prime is 38611. The next prime is 38629. The reversal of 38624 is 42683.

It is a happy number.

38624 is nontrivially palindromic in base 9.

It is a self number, because there is not a number n which added to its sum of digits gives 38624.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (38629) by changing a digit.

38624 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 (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 509 + ... + 579.

It is an arithmetic number, because the mean of its divisors is an integer number (3402).

2³⁸⁶²⁴ is an apocalyptic number.

38624 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 38624, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (40824).

38624 is an abundant number, since it is smaller than the sum of its proper divisors (43024).

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

38624 is a wasteful number, since it uses less digits than its factorization.

38624 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 98 (or 90 counting only the distinct ones).

The product of its digits is 1152, while the sum is 23.

The square root of 38624 is about 196.5298959446. The cubic root of 38624 is about 33.8027797861.

The spelling of 38624 in words is "thirty-eight thousand, six hundred twenty-four".