138585600 has 240 divisors, whose sum is σ = 509945040. Its totient is φ = 36864000.

The previous prime is 138585571. The next prime is 138585607. The reversal of 138585600 is 6585831.

138585600 is a `hidden beast` number, since 13 + 8 + 585 + 60 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (138585607) by changing a digit.

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 23 ways as a sum of consecutive naturals, for example, 345400 + ... + 345800.

It is an arithmetic number, because the mean of its divisors is an integer number (2124771).

Almost surely, 2^138585600 is an apocalyptic number.

138585600 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 138585600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (254972520).

138585600 is an abundant number, since it is smaller than the sum of its proper divisors (371359440).

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

138585600 is an equidigital number, since it uses as much as digits as its factorization.

138585600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 438 (or 411 counting only the distinct ones).

The product of its (nonzero) digits is 28800, while the sum is 36.

The square root of 138585600 is about 11772.2385296935. The cubic root of 138585600 is about 517.4948539711.

The spelling of 138585600 in words is "one hundred thirty-eight million, five hundred eighty-five thousand, six hundred".