138368 has 32 divisors (see below), whose sum is σ = 293760. Its totient is φ = 64768.

The previous prime is 138349. The next prime is 138371. The reversal of 138368 is 863831.

It is a tau number, because it is divible by the number of its divisors (32).

Its product of digits (3456) is a multiple of the sum of its prime divisors (72).

It is a self number, because there is not a number n which added to its sum of digits gives 138368.

It is an unprimeable number.

138368 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 3 ways as a sum of consecutive naturals, for example, 2921 + ... + 2967.

It is an arithmetic number, because the mean of its divisors is an integer number (9180).

2¹³⁸³⁶⁸ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 138368, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (146880).

138368 is an abundant number, since it is smaller than the sum of its proper divisors (155392).

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

138368 is an equidigital number, since it uses as much as digits as its factorization.

138368 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 84 (or 72 counting only the distinct ones).

The product of its digits is 3456, while the sum is 29.

The square root of 138368 is about 371.9784940020. The cubic root of 138368 is about 51.7223864132.

The spelling of 138368 in words is "one hundred thirty-eight thousand, three hundred sixty-eight".