864864000 has 1152 divisors, whose sum is σ = 4285532160. Its totient is φ = 165888000.

The previous prime is 864863999. The next prime is 864864023. The reversal of 864864000 is 468468.

864864000 is a `hidden beast` number, since 8 + 6 + 4 + 8 + 640 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

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

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a zygodrome in base 2.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 66527994 + ... + 66528006.

It is an arithmetic number, because the mean of its divisors is an integer number (3720080).

Almost surely, 2^864864000 is an apocalyptic number.

864864000 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 864864000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2142766080).

864864000 is an abundant number, since it is smaller than the sum of its proper divisors (3420668160).

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

864864000 is a wasteful number, since it uses less digits than its factorization.

864864000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 71 (or 41 counting only the distinct ones).

The product of its (nonzero) digits is 36864, while the sum is 36.

The square root of 864864000 is about 29408.5701794562. The cubic root of 864864000 is about 952.7580056233.

The spelling of 864864000 in words is "eight hundred sixty-four million, eight hundred sixty-four thousand".