821828000 has 192 divisors, whose sum is σ = 2358720000. Its totient is φ = 281299200.

The previous prime is 821827999. The next prime is 821828003. The reversal of 821828000 is 828128.

It is not an unprimeable number, because it can be changed into a prime (821828003) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 1371701 + ... + 1372299.

It is an arithmetic number, because the mean of its divisors is an integer number (12285000).

Almost surely, 2^821828000 is an apocalyptic number.

821828000 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 821828000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1179360000).

821828000 is an abundant number, since it is smaller than the sum of its proper divisors (1536892000).

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

821828000 is an equidigital number, since it uses as much as digits as its factorization.

821828000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 645 (or 613 counting only the distinct ones).

The product of its (nonzero) digits is 2048, while the sum is 29.

The square root of 821828000 is about 28667.5426222758. The cubic root of 821828000 is about 936.6851705135.

The spelling of 821828000 in words is "eight hundred twenty-one million, eight hundred twenty-eight thousand".