138837585600 has 1344 divisors, whose sum is σ = 620446003200. Its totient is φ = 29479403520.

The previous prime is 138837585587. The next prime is 138837585683. The reversal of 138837585600 is 6585738831.

138837585600 is a `hidden beast` number, since 1 + 3 + 8 + 8 + 3 + 75 + 8 + 560 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1344).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 580910281 + ... + 580910519.

Almost surely, 2^138837585600 is an apocalyptic number.

138837585600 is a gapful number since it is divisible by the number (10) 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 138837585600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (310223001600).

138837585600 is an abundant number, since it is smaller than the sum of its proper divisors (481608417600).

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

138837585600 is a wasteful number, since it uses less digits than its factorization.

138837585600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 407 (or 386 counting only the distinct ones).

The product of its (nonzero) digits is 4838400, while the sum is 54.

It can be divided in two parts, 138 and 837585600, that added together give a palindrome (837585738).

The spelling of 138837585600 in words is "one hundred thirty-eight billion, eight hundred thirty-seven million, five hundred eighty-five thousand, six hundred".