105585 has 8 divisors (see below), whose sum is σ = 168960. Its totient is φ = 56304.

The previous prime is 105563. The next prime is 105601. The reversal of 105585 is 585501.

It is a sphenic number, since it is the product of 3 distinct primes.

It is not a de Polignac number, because 105585 - 2¹⁰ = 104561 is a prime.

It is a super-2 number, since 2×105585² = 22296384450, which contains 22 as substring.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 3505 + ... + 3534.

It is an arithmetic number, because the mean of its divisors is an integer number (21120).

2¹⁰⁵⁵⁸⁵ is an apocalyptic number.

105585 is a gapful number since it is divisible by the number (15) formed by its first and last digit.

It is an amenable number.

105585 is a deficient number, since it is larger than the sum of its proper divisors (63375).

105585 is an equidigital number, since it uses as much as digits as its factorization.

105585 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 7047.

The product of its (nonzero) digits is 1000, while the sum is 24.

The square root of 105585 is about 324.9384557112. The cubic root of 105585 is about 47.2643919094.

It can be divided in two parts, 105 and 585, that multiplied together give a triangular number (61425 = T₃₅₀).

The spelling of 105585 in words is "one hundred five thousand, five hundred eighty-five".