180306 has 48 divisors (see below), whose sum is σ = 471744. Its totient is φ = 50544.

The previous prime is 180289. The next prime is 180307. The reversal of 180306 is 603081.

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

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 180306.

It is not an unprimeable number, because it can be changed into a prime (180307) by changing a digit.

180306 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 23 ways as a sum of consecutive naturals, for example, 3376 + ... + 3428.

It is an arithmetic number, because the mean of its divisors is an integer number (9828).

2¹⁸⁰³⁰⁶ is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 180306, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (235872).

180306 is an abundant number, since it is smaller than the sum of its proper divisors (291438).

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

180306 is an equidigital number, since it uses as much as digits as its factorization.

180306 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 77 (or 65 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

The square root of 180306 is about 424.6245400351. The cubic root of 180306 is about 56.4941388443.

Adding to 180306 its reverse (603081), we get a palindrome (783387).

The spelling of 180306 in words is "one hundred eighty thousand, three hundred six".