138313824 has 96 divisors (see below), whose sum is σ = 398514816. Its totient is φ = 41656320.

The previous prime is 138313823. The next prime is 138313831. The reversal of 138313824 is 428313831.

It is a tau number, because it is divible by the number of its divisors (96).

It is a Harshad number since it is a multiple of its sum of digits (33).

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 (138313823) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 239424 + ... + 240000.

It is an arithmetic number, because the mean of its divisors is an integer number (4151196).

Almost surely, 2^138313824 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 138313824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (199257408).

138313824 is an abundant number, since it is smaller than the sum of its proper divisors (260200992).

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

138313824 is a wasteful number, since it uses less digits than its factorization.

138313824 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 828 (or 820 counting only the distinct ones).

The product of its digits is 13824, while the sum is 33.

The square root of 138313824 is about 11760.6897756892. The cubic root of 138313824 is about 517.1563514657.

The spelling of 138313824 in words is "one hundred thirty-eight million, three hundred thirteen thousand, eight hundred twenty-four".