819040800 has 288 divisors, whose sum is σ = 2794321152. Its totient is φ = 208199680.

The previous prime is 819040799. The next prime is 819040889. The reversal of 819040800 is 8040918.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 5978332 + ... + 5978468.

It is an arithmetic number, because the mean of its divisors is an integer number (9702504).

Almost surely, 2^819040800 is an apocalyptic number.

819040800 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 819040800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1397160576).

819040800 is an abundant number, since it is smaller than the sum of its proper divisors (1975280352).

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

819040800 is a wasteful number, since it uses less digits than its factorization.

819040800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 260 (or 247 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 30.

The square root of 819040800 is about 28618.8888673198. Note that the first 4 decimals coincide. The cubic root of 819040800 is about 935.6250598503.

It can be divided in two parts, 819040 and 800, that added together give a triangular number (819840 = T₁₂₈₀).

The spelling of 819040800 in words is "eight hundred nineteen million, forty thousand, eight hundred".