45864 has 72 divisors (see below), whose sum is σ = 155610. Its totient is φ = 12096.

The previous prime is 45863. The next prime is 45869. The reversal of 45864 is 46854.

It can be written as a sum of positive squares in only one way, i.e., 44100 + 1764 = 210^2 + 42^2 .

It is a tau number, because it is divible by the number of its divisors (72).

It is a nialpdrome in base 6.

It is a zygodrome in base 6.

It is not an unprimeable number, because it can be changed into a prime (45863) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 3522 + ... + 3534.

45864 is a Friedman number, since it can be written as 546*84, using all its digits and the basic arithmetic operations.

2⁴⁵⁸⁶⁴ 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 45864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (77805).

45864 is an abundant number, since it is smaller than the sum of its proper divisors (109746).

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

45864 is a wasteful number, since it uses less digits than its factorization.

45864 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 39 (or 25 counting only the distinct ones).

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

The square root of 45864 is about 214.1588195709. The cubic root of 45864 is about 35.7951326570.

Subtracting from 45864 its product of digits (3840), we obtain a palindrome (42024).

Subtracting 45864 from its reverse (46854), we obtain a triangular number (990 = T₄₄).

It can be divided in two parts, 45 and 864, that added together give a palindrome (909).

The spelling of 45864 in words is "forty-five thousand, eight hundred sixty-four".