216864 has 48 divisors (see below), whose sum is σ = 635040. Its totient is φ = 72000.

The previous prime is 216859. The next prime is 216877. The reversal of 216864 is 468612.

It is a tau number, because it is divible by the number of its divisors (48).

It is a Smith number, since the sum of its digits (27) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (27).

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

It is an Ulam number.

Its product of digits (2304) is a multiple of the sum of its prime divisors (256).

It is an unprimeable number.

216864 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 7 ways as a sum of consecutive naturals, for example, 739 + ... + 989.

It is an arithmetic number, because the mean of its divisors is an integer number (13230).

2²¹⁶⁸⁶⁴ is an apocalyptic number.

216864 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 216864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (317520).

216864 is an abundant number, since it is smaller than the sum of its proper divisors (418176).

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

216864 is a wasteful number, since it uses less digits than its factorization.

216864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 270 (or 256 counting only the distinct ones).

The product of its digits is 2304, while the sum is 27.

The square root of 216864 is about 465.6865898864. The cubic root of 216864 is about 60.0798935697.

It can be divided in two parts, 216 and 864, that multiplied together give a square (186624 = 432²).

The spelling of 216864 in words is "two hundred sixteen thousand, eight hundred sixty-four".