82321588224 has 720 divisors, whose sum is σ = 274802411520. Its totient is φ = 24524881920.

The previous prime is 82321588187. The next prime is 82321588229. The reversal of 82321588224 is 42288512328.

82321588224 is a `hidden beast` number, since 8 + 23 + 21 + 588 + 2 + 24 = 666.

It is a self number, because there is not a number n which added to its sum of digits gives 82321588224.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82321588229) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 2655535089 + ... + 2655535119.

It is an arithmetic number, because the mean of its divisors is an integer number (381670016).

Almost surely, 2^82321588224 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 82321588224, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (137401205760).

82321588224 is an abundant number, since it is smaller than the sum of its proper divisors (192480823296).

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

82321588224 is an equidigital number, since it uses as much as digits as its factorization.

82321588224 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 126 (or 88 counting only the distinct ones).

The product of its digits is 491520, while the sum is 45.

The spelling of 82321588224 in words is "eighty-two billion, three hundred twenty-one million, five hundred eighty-eight thousand, two hundred twenty-four".