90585 has 32 divisors (see below), whose sum is σ = 178560. Its totient is φ = 43200.

The previous prime is 90583. The next prime is 90599. The reversal of 90585 is 58509.

It is not a de Polignac number, because 90585 - 2¹ = 90583 is a prime.

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

It is an alternating number because its digits alternate between odd and even.

It is not an unprimeable number, because it can be changed into a prime (90583) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 1455 + ... + 1515.

It is an arithmetic number, because the mean of its divisors is an integer number (5580).

2⁹⁰⁵⁸⁵ is an apocalyptic number.

It is an amenable number.

90585 is a deficient number, since it is larger than the sum of its proper divisors (87975).

90585 is a wasteful number, since it uses less digits than its factorization.

90585 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 86 (or 80 counting only the distinct ones).

The product of its (nonzero) digits is 1800, while the sum is 27.

The square root of 90585 is about 300.9734207534. The cubic root of 90585 is about 44.9109349478.

It can be divided in two parts, 905 and 85, that added together give a triangular number (990 = T₄₄).

The spelling of 90585 in words is "ninety thousand, five hundred eighty-five".