138024 has 48 divisors (see below), whose sum is σ = 393120. Its totient is φ = 45360.

The previous prime is 138007. The next prime is 138041. The reversal of 138024 is 420831.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (138007) and next prime (138041).

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

It is a junction number, because it is equal to n+sod(n) for n = 137988 and 138006.

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 138024.

It is an unprimeable number.

138024 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 (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1909 + ... + 1979.

It is an arithmetic number, because the mean of its divisors is an integer number (8190).

2¹³⁸⁰²⁴ 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 138024, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (196560).

138024 is an abundant number, since it is smaller than the sum of its proper divisors (255096).

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

138024 is an equidigital number, since it uses as much as digits as its factorization.

138024 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 92 (or 76 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 138024 is about 371.5158139299. The cubic root of 138024 is about 51.6794880887.

Adding to 138024 its reverse (420831), we get a palindrome (558855).

It can be divided in two parts, 1 and 38024, that added together give a square (38025 = 195²).

The spelling of 138024 in words is "one hundred thirty-eight thousand, twenty-four".