138384 has 45 divisors (see below), whose sum is σ = 400179. Its totient is φ = 44640.

The previous prime is 138373. The next prime is 138389. The reversal of 138384 is 483831.

138384 = T₃₇₁ + T₃₇₂.

The square root of 138384 is 372.

It is a perfect power (a square), and thus also a powerful number.

It is a nude number because it is divisible by every one of its digits.

Its product of digits (2304) is a multiple of the sum of its prime divisors (36).

It is not an unprimeable number, because it can be changed into a prime (138389) by changing a digit.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 4449 + ... + 4479.

2¹³⁸³⁸⁴ is an apocalyptic number.

138384 is the 372-nd square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 138384

138384 is an abundant number, since it is smaller than the sum of its proper divisors (261795).

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

138384 is a wasteful number, since it uses less digits than its factorization.

138384 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 76 (or 36 counting only the distinct ones).

The product of its digits is 2304, while the sum is 27.

The cubic root of 138384 is about 51.7243799529.

Multiplying 138384 by its product of digits (2304), we get a square (318836736 = 17856²).

The spelling of 138384 in words is "one hundred thirty-eight thousand, three hundred eighty-four".