813866400 has 288 divisors, whose sum is σ = 3018556800. Its totient is φ = 211507200.

The previous prime is 813866369. The next prime is 813866401. The reversal of 813866400 is 4668318.

It is a happy number.

813866400 is a `hidden beast` number, since 8 + 1 + 3 + 8 + 6 + 640 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

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

It is not an unprimeable number, because it can be changed into a prime (813866401) by changing a digit.

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 47 ways as a sum of consecutive naturals, for example, 885141 + ... + 886059.

It is an arithmetic number, because the mean of its divisors is an integer number (10481100).

Almost surely, 2^813866400 is an apocalyptic number.

813866400 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 813866400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1509278400).

813866400 is an abundant number, since it is smaller than the sum of its proper divisors (2204690400).

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

813866400 is a wasteful number, since it uses less digits than its factorization.

813866400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 989 (or 970 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 36.

The square root of 813866400 is about 28528.3438005083. The cubic root of 813866400 is about 933.6505837608.

The spelling of 813866400 in words is "eight hundred thirteen million, eight hundred sixty-six thousand, four hundred".