138384000000 has 693 divisors, whose sum is σ = 516101264913. Its totient is φ = 35712000000.

The previous prime is 138383999993. The next prime is 138384000023. The reversal of 138384000000 is 483831.

The square root of 138384000000 is 372000.

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

It can be written as a sum of positive squares in 3 ways, for example, as 121237668864 + 17146331136 = 348192^2 + 130944^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 62 ways as a sum of consecutive naturals, for example, 4463999985 + ... + 4464000015.

Almost surely, 2^138384000000 is an apocalyptic number.

138384000000 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

138384000000 is the 372000-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 138384000000

138384000000 is an abundant number, since it is smaller than the sum of its proper divisors (377717264913).

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

138384000000 is an frugal number, since it uses more digits than its factorization.

138384000000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 118 (or 41 counting only the distinct ones).

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

Multiplying 138384000000 by its product of nonzero digits (2304), we get a square (318836736000000 = 17856000²).

138384000000 divided by its product of nonzero digits (2304) gives a square (60062500 = 7750²).

Adding to 138384000000 its reverse (483831), we get a palindrome (138384483831).

The spelling of 138384000000 in words is "one hundred thirty-eight billion, three hundred eighty-four million", and thus it is an aban number.