13185165312 has 384 divisors, whose sum is σ = 43518384000. Its totient is φ = 3910533120.

The previous prime is 13185165251. The next prime is 13185165313. The reversal of 13185165312 is 21356158131.

It is a happy number.

13185165312 is a `hidden beast` number, since 1 + 3 + 185 + 165 + 312 = 666.

It is a tau number, because it is divible by the number of its divisors (384).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (13185165313) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 32237364 + ... + 32237772.

It is an arithmetic number, because the mean of its divisors is an integer number (113329125).

Almost surely, 2^13185165312 is an apocalyptic number.

13185165312 is a gapful number since it is divisible by the number (12) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 13185165312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (21759192000).

13185165312 is an abundant number, since it is smaller than the sum of its proper divisors (30333218688).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

13185165312 is a wasteful number, since it uses less digits than its factorization.

13185165312 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 504 (or 478 counting only the distinct ones).

The product of its digits is 21600, while the sum is 36.

The spelling of 13185165312 in words is "thirteen billion, one hundred eighty-five million, one hundred sixty-five thousand, three hundred twelve".