864 has 24 divisors (see below), whose sum is σ = 2520. Its totient is φ = 288.

The previous prime is 863. The next prime is 877. The reversal of 864 is 468.

It can be divided in two parts, 8 and 64, that multiplied together give a 9-th power (512 = 2^{9}).

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 Jordan-Polya number, since it can be written as 4! ⋅ (3!)^{2}.

864 is an esthetic number in base 7, because in such base its adjacent digits differ by 1.

It is a tau number, because it is divible by the number of its divisors (24).

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

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

It is an Ulam number.

It is one of the 548 Lynch-Bell numbers.

It is a straight-line number, since its digits are in arithmetic progression.

It is a plaindrome in base 14.

It is a nialpdrome in base 6, base 10 and base 12.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (863) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 287 + 288 + 289.

It is an arithmetic number, because the mean of its divisors is an integer number (105).

2^{864} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1260).

864 is an abundant number, since it is smaller than the sum of its proper divisors (1656).

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

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

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

The sum of its prime factors is 19 (or 5 counting only the distinct ones).

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

The square root of 864 is about 29.3938769134. The cubic root of 864 is about 9.5244063118.

The spelling of 864 in words is "eight hundred sixty-four", and thus it is an aban number.

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