864000 has 144 divisors (see below), whose sum is σ = 3188640. Its totient is φ = 230400.

The previous prime is 863983. The next prime is 864007. The reversal of 864000 is 468.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a tau number, because it is divible by the number of its divisors (144).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an Ulam number.

It is a nialpdrome in base 10.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (864007) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 172798 + ... + 172802.

2⁸⁶⁴⁰⁰⁰ is an apocalyptic number.

864000 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 864000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1594320).

864000 is an abundant number, since it is smaller than the sum of its proper divisors (2324640).

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

864000 is an equidigital number, since it uses as much as digits as its factorization.

864000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 40 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 864000 is about 929.5160030898. The cubic root of 864000 is about 95.2440631181.

Adding to 864000 its reverse (468), we get a palindrome (864468).

It can be divided in two parts, 8 and 64000, that multiplied together give a cube (512000 = 80³).

The spelling of 864000 in words is "eight hundred sixty-four thousand".