288864 has 72 divisors (see below), whose sum is σ = 884520. Its totient is φ = 89088.

The previous prime is 288853. The next prime is 288877. The reversal of 288864 is 468882.

It is a tau number, because it is divible by the number of its divisors (72).

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

It is a nude number because it is divisible by every one of its digits.

288864 is a modest number, since divided by 864 gives 288 as remainder.

It is a congruent number.

It is an unprimeable number.

288864 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 4867 + ... + 4925.

It is an arithmetic number, because the mean of its divisors is an integer number (12285).

2²⁸⁸⁸⁶⁴ is an apocalyptic number.

288864 is a gapful number since it is divisible by the number (24) 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 288864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (442260).

288864 is an abundant number, since it is smaller than the sum of its proper divisors (595656).

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

288864 is a wasteful number, since it uses less digits than its factorization.

288864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 92 (or 81 counting only the distinct ones).

The product of its digits is 24576, while the sum is 36.

The square root of 288864 is about 537.4606962374. The cubic root of 288864 is about 66.1045175942.

It can be divided in two parts, 288 and 864, that multiplied together give a 5-th power (248832 = 12⁵).

The spelling of 288864 in words is "two hundred eighty-eight thousand, eight hundred sixty-four".