13185 has 12 divisors (see below), whose sum is σ = 22932. Its totient is φ = 7008.

The previous prime is 13183. The next prime is 13187. The reversal of 13185 is 58131.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (13183) and next prime (13187).

It can be written as a sum of positive squares in 2 ways, for example, as 9216 + 3969 = 96^2 + 63^2 .

It is not a de Polignac number, because 13185 - 2¹ = 13183 is a prime.

It is a Curzon number.

It is not an unprimeable number, because it can be changed into a prime (13183) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 102 + ... + 191.

It is an arithmetic number, because the mean of its divisors is an integer number (1911).

It is a Proth number, since it is equal to 103 ⋅ 2⁷ + 1 and 103 < 2⁷.

2¹³¹⁸⁵ is an apocalyptic number.

13185 is a gapful number since it is divisible by the number (15) formed by its first and last digit.

It is an amenable number.

13185 is a deficient number, since it is larger than the sum of its proper divisors (9747).

13185 is a wasteful number, since it uses less digits than its factorization.

13185 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 304 (or 301 counting only the distinct ones).

The product of its digits is 120, while the sum is 18.

The square root of 13185 is about 114.8259552540. The cubic root of 13185 is about 23.6243596030.

Adding to 13185 its sum of digits (18), we get a triangular number (13203 = T₁₆₂).

It can be divided in two parts, 131 and 85, that added together give a cube (216 = 6³).

The spelling of 13185 in words is "thirteen thousand, one hundred eighty-five".