180090 has 64 divisors (see below), whose sum is σ = 518400. Its totient is φ = 44352.

The previous prime is 180077. The next prime is 180097. The reversal of 180090 is 90081.

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

It is a Curzon number.

It is a plaindrome in base 11.

It is not an unprimeable number, because it can be changed into a prime (180097) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 6196 + ... + 6224.

It is an arithmetic number, because the mean of its divisors is an integer number (8100).

2¹⁸⁰⁰⁹⁰ is an apocalyptic number.

180090 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is a practical number, because each smaller number is the sum of distinct divisors of 180090, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (259200).

180090 is an abundant number, since it is smaller than the sum of its proper divisors (338310).

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

180090 is a wasteful number, since it uses less digits than its factorization.

180090 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 68 (or 62 counting only the distinct ones).

The product of its (nonzero) digits is 72, while the sum is 18.

The square root of 180090 is about 424.3701214742. The cubic root of 180090 is about 56.4715705252.

Subtracting from 180090 its reverse (90081), we obtain a palindrome (90009).

The spelling of 180090 in words is "one hundred eighty thousand, ninety".