45180 has 36 divisors (see below), whose sum is σ = 137592. Its totient is φ = 12000.

The previous prime is 45179. The next prime is 45181. The reversal of 45180 is 8154.

45180 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (45179) and next prime (45181).

It is a tau number, because it is divible by the number of its divisors (36).

It is a hoax number, since the sum of its digits (18) coincides with the sum of the digits of its distinct prime factors.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (45181) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 55 + ... + 305.

It is an arithmetic number, because the mean of its divisors is an integer number (3822).

2⁴⁵¹⁸⁰ 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 45180, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (68796).

45180 is an abundant number, since it is smaller than the sum of its proper divisors (92412).

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

45180 is a wasteful number, since it uses less digits than its factorization.

45180 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 266 (or 261 counting only the distinct ones).

The product of its (nonzero) digits is 160, while the sum is 18.

The square root of 45180 is about 212.5558750070. Note that the first 3 decimals coincide. The cubic root of 45180 is about 35.6162951954.

It can be divided in two parts, 45 and 180, that multiplied together give a square (8100 = 90²).

The spelling of 45180 in words is "forty-five thousand, one hundred eighty".