821009952 has 384 divisors, whose sum is σ = 2941747200. Its totient is φ = 217728000.

The previous prime is 821009899. The next prime is 821009963. The reversal of 821009952 is 259900128.

821009952 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

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 63 ways as a sum of consecutive naturals, for example, 5437077 + ... + 5437227.

It is an arithmetic number, because the mean of its divisors is an integer number (7660800).

Almost surely, 2^821009952 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 821009952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1470873600).

821009952 is an abundant number, since it is smaller than the sum of its proper divisors (2120737248).

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

821009952 is a wasteful number, since it uses less digits than its factorization.

821009952 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 237 (or 223 counting only the distinct ones).

The product of its (nonzero) digits is 12960, while the sum is 36.

The square root of 821009952 is about 28653.2712268599. The cubic root of 821009952 is about 936.3742750406.

The spelling of 821009952 in words is "eight hundred twenty-one million, nine thousand, nine hundred fifty-two".