180864 has 48 divisors (see below), whose sum is σ = 523770. Its totient is φ = 59904.

The previous prime is 180847. The next prime is 180871. The reversal of 180864 is 468081.

It can be written as a sum of positive squares in only one way, i.e., 166464 + 14400 = 408^2 + 120^2 .

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

It is a nialpdrome in base 12.

It is a zygodrome in base 12.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 180864.

It is an unprimeable number.

180864 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 1074 + ... + 1230.

2¹⁸⁰⁸⁶⁴ 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 180864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (261885).

180864 is an abundant number, since it is smaller than the sum of its proper divisors (342906).

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

180864 is a wasteful number, since it uses less digits than its factorization.

180864 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 177 (or 162 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 27.

The square root of 180864 is about 425.2810835201. The cubic root of 180864 is about 56.5523570327.

The spelling of 180864 in words is "one hundred eighty thousand, eight hundred sixty-four".