821261331072 has 1024 divisors, whose sum is σ = 3074198400000. Its totient is φ = 214462660608.

The previous prime is 821261331053. The next prime is 821261331073. The reversal of 821261331072 is 270133162128.

821261331072 is a `hidden beast` number, since 8 + 2 + 1 + 2 + 613 + 31 + 0 + 7 + 2 = 666.

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 (821261331073) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 2111211454 + ... + 2111211842.

It is an arithmetic number, because the mean of its divisors is an integer number (3002146875).

Almost surely, 2^821261331072 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 821261331072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1537099200000).

821261331072 is an abundant number, since it is smaller than the sum of its proper divisors (2252937068928).

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

821261331072 is a wasteful number, since it uses less digits than its factorization.

821261331072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 583 (or 551 counting only the distinct ones).

The product of its (nonzero) digits is 24192, while the sum is 36.

The spelling of 821261331072 in words is "eight hundred twenty-one billion, two hundred sixty-one million, three hundred thirty-one thousand, seventy-two".