813004800 has 288 divisors, whose sum is σ = 2762323200. Its totient is φ = 210862080.

The previous prime is 813004793. The next prime is 813004817. The reversal of 813004800 is 8400318.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 10291161 + ... + 10291239.

It is an arithmetic number, because the mean of its divisors is an integer number (9591400).

Almost surely, 2^813004800 is an apocalyptic number.

813004800 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 813004800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1381161600).

813004800 is an abundant number, since it is smaller than the sum of its proper divisors (1949318400).

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

813004800 is a wasteful number, since it uses less digits than its factorization.

813004800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 181 (or 156 counting only the distinct ones).

The product of its (nonzero) digits is 768, while the sum is 24.

The square root of 813004800 is about 28513.2390303171. The cubic root of 813004800 is about 933.3209975694.

The spelling of 813004800 in words is "eight hundred thirteen million, four thousand, eight hundred".