33180 has 48 divisors (see below), whose sum is σ = 107520. Its totient is φ = 7488.

The previous prime is 33179. The next prime is 33181. The reversal of 33180 is 8133.

It is an interprime number because it is at equal distance from previous prime (33179) and next prime (33181).

It is a super-2 number, since 2×33180² = 2201824800, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 33180.

It is not an unprimeable number, because it can be changed into a prime (33181) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 381 + ... + 459.

It is an arithmetic number, because the mean of its divisors is an integer number (2240).

2³³¹⁸⁰ is an apocalyptic number.

33180 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 33180, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (53760).

33180 is an abundant number, since it is smaller than the sum of its proper divisors (74340).

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

33180 is a wasteful number, since it uses less digits than its factorization.

33180 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 98 (or 96 counting only the distinct ones).

The product of its (nonzero) digits is 72, while the sum is 15.

The square root of 33180 is about 182.1537811850. The cubic root of 33180 is about 32.1335563919.

The spelling of 33180 in words is "thirty-three thousand, one hundred eighty".