180768 has 48 divisors (see below), whose sum is σ = 544320. Its totient is φ = 51456.

The previous prime is 180751. The next prime is 180773. The reversal of 180768 is 867081.

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 an unprimeable number.

180768 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 7 ways as a sum of consecutive naturals, for example, 538 + ... + 806.

It is an arithmetic number, because the mean of its divisors is an integer number (11340).

2¹⁸⁰⁷⁶⁸ 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 180768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (272160).

180768 is an abundant number, since it is smaller than the sum of its proper divisors (363552).

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

180768 is a wasteful number, since it uses less digits than its factorization.

180768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 289 (or 281 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 30.

The square root of 180768 is about 425.1682020095. The cubic root of 180768 is about 56.5423495370.

The spelling of 180768 in words is "one hundred eighty thousand, seven hundred sixty-eight".