813888000 has 400 divisors, whose sum is σ = 3051003384. Its totient is φ = 215654400.

The previous prime is 813887969. The next prime is 813888011. The reversal of 813888000 is 888318.

It can be written as a sum of positive squares in 4 ways, for example, as 164249856 + 649638144 = 12816^2 + 25488^2 .

It is a tau number, because it is divible by the number of its divisors (400).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 5183922 + ... + 5184078.

Almost surely, 2^813888000 is an apocalyptic number.

813888000 is a gapful number since it is divisible by the number (80) 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 813888000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1525501692).

813888000 is an abundant number, since it is smaller than the sum of its proper divisors (2237115384).

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

813888000 is an equidigital number, since it uses as much as digits as its factorization.

813888000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 202 (or 167 counting only the distinct ones).

The product of its (nonzero) digits is 12288, while the sum is 36.

The square root of 813888000 is about 28528.7223688689. The cubic root of 813888000 is about 933.6588433778.

The spelling of 813888000 in words is "eight hundred thirteen million, eight hundred eighty-eight thousand".