90624 has 40 divisors (see below), whose sum is σ = 245520. Its totient is φ = 29696.

The previous prime is 90619. The next prime is 90631. The reversal of 90624 is 42609.

90624 is nontrivially palindromic in base 14.

It is a trimorphic number since its cube, 744268574490624, ends in 90624.

It is a self number, because there is not a number n which added to its sum of digits gives 90624.

It is an unprimeable number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 1507 + ... + 1565.

It is an arithmetic number, because the mean of its divisors is an integer number (6138).

2⁹⁰⁶²⁴ 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 90624, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (122760).

90624 is an abundant number, since it is smaller than the sum of its proper divisors (154896).

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

90624 is an equidigital number, since it uses as much as digits as its factorization.

90624 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 80 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 432, while the sum is 21.

The square root of 90624 is about 301.0382035556. The cubic root of 90624 is about 44.9173792640.

The spelling of 90624 in words is "ninety thousand, six hundred twenty-four".