138312 has 48 divisors (see below), whose sum is σ = 400140. Its totient is φ = 43008.

The previous prime is 138311. The next prime is 138319. The reversal of 138312 is 213831.

It can be written as a sum of positive squares in 2 ways, for example, as 133956 + 4356 = 366^2 + 66^2 .

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (138311) 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, 1168 + ... + 1280.

2¹³⁸³¹² is an apocalyptic number.

138312 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 138312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (200070).

138312 is an abundant number, since it is smaller than the sum of its proper divisors (261828).

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

138312 is a wasteful number, since it uses less digits than its factorization.

138312 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 142 (or 135 counting only the distinct ones).

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

The square root of 138312 is about 371.9032132155. The cubic root of 138312 is about 51.7154078140.

The spelling of 138312 in words is "one hundred thirty-eight thousand, three hundred twelve".