33705 has 24 divisors (see below), whose sum is σ = 67392. Its totient is φ = 15264.

The previous prime is 33703. The next prime is 33713. The reversal of 33705 is 50733.

It is not a de Polignac number, because 33705 - 2¹ = 33703 is a prime.

It is a super-2 number, since 2×33705² = 2272054050, which contains 22 as substring.

It is a Curzon number.

33705 is a lucky number.

It is a plaindrome in base 13.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 33705.

It is not an unprimeable number, because it can be changed into a prime (33703) 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 23 ways as a sum of consecutive naturals, for example, 262 + ... + 368.

It is an arithmetic number, because the mean of its divisors is an integer number (2808).

2³³⁷⁰⁵ is an apocalyptic number.

33705 is a gapful number since it is divisible by the number (35) formed by its first and last digit.

It is an amenable number.

33705 is a deficient number, since it is larger than the sum of its proper divisors (33687).

33705 is a wasteful number, since it uses less digits than its factorization.

33705 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 125 (or 122 counting only the distinct ones).

The product of its (nonzero) digits is 315, while the sum is 18.

The square root of 33705 is about 183.5892153695. The cubic root of 33705 is about 32.3021510643.

It can be divided in two parts, 3370 and 5, that added together give a cube (3375 = 15³).

The spelling of 33705 in words is "thirty-three thousand, seven hundred five".