820965600 has 648 divisors, whose sum is σ = 3646875960. Its totient is φ = 172247040.

The previous prime is 820965599. The next prime is 820965641. The reversal of 820965600 is 6569028.

820965600 is a `hidden beast` number, since 8 + 2 + 0 + 96 + 560 + 0 = 666.

820965600 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 a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 107 ways as a sum of consecutive naturals, for example, 4586311 + ... + 4586489.

It is an arithmetic number, because the mean of its divisors is an integer number (5627895).

Almost surely, 2^820965600 is an apocalyptic number.

820965600 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 820965600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1823437980).

820965600 is an abundant number, since it is smaller than the sum of its proper divisors (2825910360).

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

820965600 is a wasteful number, since it uses less digits than its factorization.

820965600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 232 (or 209 counting only the distinct ones).

The product of its (nonzero) digits is 25920, while the sum is 36.

The square root of 820965600 is about 28652.4972733617. The cubic root of 820965600 is about 936.3574133612.

The spelling of 820965600 in words is "eight hundred twenty million, nine hundred sixty-five thousand, six hundred".