827164800 has 576 divisors, whose sum is σ = 3689674560. Its totient is φ = 171417600.

The previous prime is 827164777. The next prime is 827164817. The reversal of 827164800 is 8461728.

827164800 is a `hidden beast` number, since 8 + 2 + 7 + 1 + 648 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (576).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 2217414 + ... + 2217786.

It is an arithmetic number, because the mean of its divisors is an integer number (6405685).

Almost surely, 2^827164800 is an apocalyptic number.

827164800 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 827164800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1844837280).

827164800 is an abundant number, since it is smaller than the sum of its proper divisors (2862509760).

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

827164800 is a wasteful number, since it uses less digits than its factorization.

827164800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 421 (or 401 counting only the distinct ones).

The product of its (nonzero) digits is 21504, while the sum is 36.

The square root of 827164800 is about 28760.4728751111. The cubic root of 827164800 is about 938.7083512107.

The spelling of 827164800 in words is "eight hundred twenty-seven million, one hundred sixty-four thousand, eight hundred".