820805678578800 has 540 divisors, whose sum is σ = 2954217244881240. Its totient is φ = 211033143014400.

The previous prime is 820805678578751. The next prime is 820805678578931. The reversal of 820805678578800 is 8875876508028.

820805678578800 is a `hidden beast` number, since 8 + 2 + 0 + 8 + 0 + 567 + 8 + 57 + 8 + 8 + 0 + 0 = 666.

It is a hoax number, since the sum of its digits (72) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (72).

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, 930191407 + ... + 931073393.

It is an arithmetic number, because the mean of its divisors is an integer number (5470772675706).

Almost surely, 2^{820805678578800} is an apocalyptic number.

820805678578800 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 820805678578800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1477108622440620).

820805678578800 is an abundant number, since it is smaller than the sum of its proper divisors (2133411566302440).

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

820805678578800 is a wasteful number, since it uses less digits than its factorization.

820805678578800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 882342 (or 882297 counting only the distinct ones).

The product of its (nonzero) digits is 481689600, while the sum is 72.

The spelling of 820805678578800 in words is "eight hundred twenty trillion, eight hundred five billion, six hundred seventy-eight million, five hundred seventy-eight thousand, eight hundred".