45585 has 12 divisors (see below), whose sum is σ = 79092. Its totient is φ = 24288.

The previous prime is 45569. The next prime is 45587. The reversal of 45585 is 58554.

It can be written as a sum of positive squares in 2 ways, for example, as 5184 + 40401 = 72^2 + 201^2 .

It is not a de Polignac number, because 45585 - 2⁴ = 45569 is a prime.

It is a plaindrome in base 12.

It is a nialpdrome in base 16.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (45587) 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, 462 + ... + 551.

It is an arithmetic number, because the mean of its divisors is an integer number (6591).

It is the magic constant of a 45 × 45 magic square.

2⁴⁵⁵⁸⁵ is an apocalyptic number.

45585 is a gapful number since it is divisible by the number (45) formed by its first and last digit.

It is an amenable number.

45585 is a deficient number, since it is larger than the sum of its proper divisors (33507).

45585 is a wasteful number, since it uses less digits than its factorization.

45585 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1024 (or 1021 counting only the distinct ones).

The product of its digits is 4000, while the sum is 27.

The square root of 45585 is about 213.5064401839. The cubic root of 45585 is about 35.7224019649.

It can be divided in two parts, 45 and 585, that added together give a triangular number (630 = T₃₅).

The spelling of 45585 in words is "forty-five thousand, five hundred eighty-five".