4185 has 16 divisors (see below), whose sum is σ = 7680. Its totient is φ = 2160.

The previous prime is 4177. The next prime is 4201. The reversal of 4185 is 5814.

4185 is nontrivially palindromic in base 6.

It is not a de Polignac number, because 4185 - 2³ = 4177 is a prime.

It is a Smith number, since the sum of its digits (18) coincides with the sum of the digits of its prime factors.

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

It is a congruent number.

It is an unprimeable number.

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 15 ways as a sum of consecutive naturals, for example, 120 + ... + 150.

It is an arithmetic number, because the mean of its divisors is an integer number (480).

2⁴¹⁸⁵ is an apocalyptic number.

4185 is a gapful number since it is divisible by the number (45) formed by its first and last digit.

It is an amenable number.

4185 is a deficient number, since it is larger than the sum of its proper divisors (3495).

4185 is a wasteful number, since it uses less digits than its factorization.

With its successor (4186) it forms a Ruth-Aaron pair, since the sum of their prime factors is the same (45).

4185 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 45 (or 39 counting only the distinct ones).

The product of its digits is 160, while the sum is 18.

The square root of 4185 is about 64.6915759585. The cubic root of 4185 is about 16.1150560648.

Adding to 4185 its reverse (5814), we get a palindrome (9999).

The spelling of 4185 in words is "four thousand, one hundred eighty-five".