38160 has 60 divisors (see below), whose sum is σ = 130572. Its totient is φ = 9984.

The previous prime is 38153. The next prime is 38167. The reversal of 38160 is 6183.

It is an interprime number because it is at equal distance from previous prime (38153) and next prime (38167).

It can be written as a sum of positive squares in 2 ways, for example, as 20736 + 17424 = 144^2 + 132^2 .

It is a tau number, because it is divible by the number of its divisors (60).

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

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 16.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 38160.

It is not an unprimeable number, because it can be changed into a prime (38167) by changing a digit.

38160 is an untouchable number, because it is not equal to the sum of proper divisors of any 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 11 ways as a sum of consecutive naturals, for example, 694 + ... + 746.

2³⁸¹⁶⁰ is an apocalyptic number.

38160 is a gapful number since it is divisible by the number (30) 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 38160, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (65286).

38160 is an abundant number, since it is smaller than the sum of its proper divisors (92412).

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

38160 is a wasteful number, since it uses less digits than its factorization.

38160 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 72 (or 63 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

The square root of 38160 is about 195.3458471532. The cubic root of 38160 is about 33.6668736168. Note that the first 3 decimals are identical.

It can be divided in two parts, 381 and 60, that added together give a square (441 = 21²).

The spelling of 38160 in words is "thirty-eight thousand, one hundred sixty".