820657992960 has 720 divisors, whose sum is σ = 3195456748176. Its totient is φ = 199893712896.

The previous prime is 820657992953. The next prime is 820657992989. The reversal of 820657992960 is 69299756028.

820657992960 is a `hidden beast` number, since 8 + 206 + 57 + 99 + 296 + 0 = 666.

It can be written as a sum of positive squares in 8 ways, for example, as 517653504 + 820140339456 = 22752^2 + 905616^2 .

It is a tau number, because it is divible by the number of its divisors (720).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 130737342 + ... + 130743618.

Almost surely, 2^820657992960 is an apocalyptic number.

820657992960 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 820657992960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1597728374088).

820657992960 is an abundant number, since it is smaller than the sum of its proper divisors (2374798755216).

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

820657992960 is a wasteful number, since it uses less digits than its factorization.

820657992960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 6420 (or 6397 counting only the distinct ones).

The product of its (nonzero) digits is 29393280, while the sum is 63.

The spelling of 820657992960 in words is "eight hundred twenty billion, six hundred fifty-seven million, nine hundred ninety-two thousand, nine hundred sixty".