1585 has 4 divisors (see below), whose sum is σ = 1908. Its totient is φ = 1264.

The previous prime is 1583. The next prime is 1597. The reversal of 1585 is 5851.

1585 = T₃₁ + T₃₂ + T₃₃.

It is a semiprime because it is the product of two primes.

It can be written as a sum of positive squares in 2 ways, for example, as 289 + 1296 = 17^2 + 36^2 .

It is a cyclic number.

It is not a de Polignac number, because 1585 - 2¹ = 1583 is a prime.

It is a Duffinian number.

1585 is a lucky number.

It is a nialpdrome in base 16.

It is not an unprimeable number, because it can be changed into a prime (1583) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 154 + ... + 163.

It is an arithmetic number, because the mean of its divisors is an integer number (477).

1585 is the 33-rd centered triangular number.

It is an amenable number.

1585 is a deficient number, since it is larger than the sum of its proper divisors (323).

1585 is an equidigital number, since it uses as much as digits as its factorization.

1585 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 322.

The product of its digits is 200, while the sum is 19.

The square root of 1585 is about 39.8120584748. The cubic root of 1585 is about 11.6594059130.

It can be divided in two parts, 15 and 85, that multiplied together give a triangular number (1275 = T₅₀).

The spelling of 1585 in words is "one thousand, five hundred eighty-five".