45684 has 36 divisors (see below), whose sum is σ = 122304. Its totient is φ = 14904.

The previous prime is 45677. The next prime is 45691. The reversal of 45684 is 48654.

45684 is digitally balanced in base 2 and base 4, because in such bases 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 (45677) and next prime (45691).

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

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an Ulam number.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 949 + ... + 995.

45684 is a Friedman number, since it can be written as 846*54, using all its digits and the basic arithmetic operations.

2⁴⁵⁶⁸⁴ 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 45684, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (61152).

45684 is an abundant number, since it is smaller than the sum of its proper divisors (76620).

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

45684 is a wasteful number, since it uses less digits than its factorization.

45684 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 66 (or 52 counting only the distinct ones).

The product of its digits is 3840, while the sum is 27.

The square root of 45684 is about 213.7381575667. The cubic root of 45684 is about 35.7482435116.

It can be divided in two parts, 45 and 684, that added together give a 6-th power (729 = 3⁶).

The spelling of 45684 in words is "forty-five thousand, six hundred eighty-four".