864144000 has 384 divisors, whose sum is σ = 3295216080. Its totient is φ = 216268800.

The previous prime is 864143999. The next prime is 864144013. The reversal of 864144000 is 441468.

It can be written as a sum of positive squares in 8 ways, for example, as 66194496 + 797949504 = 8136^2 + 28248^2 .

It is a tau number, because it is divible by the number of its divisors (384).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 2447824 + ... + 2448176.

Almost surely, 2^864144000 is an apocalyptic number.

864144000 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 864144000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1647608040).

864144000 is an abundant number, since it is smaller than the sum of its proper divisors (2431072080).

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

864144000 is a wasteful number, since it uses less digits than its factorization.

864144000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 405 (or 380 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 27.

The square root of 864144000 is about 29396.3263010874. The cubic root of 864144000 is about 952.4935416100.

Adding to 864144000 its reverse (441468), we get a palindrome (864585468).

The spelling of 864144000 in words is "eight hundred sixty-four million, one hundred forty-four thousand".