821164032 has 288 divisors, whose sum is σ = 2683044000. Its totient is φ = 240058368.

The previous prime is 821163979. The next prime is 821164063. The reversal of 821164032 is 230461128.

821164032 is a `hidden beast` number, since 8 + 2 + 11 + 640 + 3 + 2 = 666.

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

It is a zygodrome in base 2.

It is a junction number, because it is equal to n+sod(n) for n = 821163987 and 821164005.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 5511094 + ... + 5511242.

It is an arithmetic number, because the mean of its divisors is an integer number (9316125).

Almost surely, 2^821164032 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 821164032, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1341522000).

821164032 is an abundant number, since it is smaller than the sum of its proper divisors (1861879968).

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

821164032 is a wasteful number, since it uses less digits than its factorization.

821164032 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 213 (or 190 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 821164032 is about 28655.9597989668. The cubic root of 821164032 is about 936.4328482338.

Adding to 821164032 its product of nonzero digits (2304), we get a square (821166336 = 28656²).

The spelling of 821164032 in words is "eight hundred twenty-one million, one hundred sixty-four thousand, thirty-two".