138085200 has 270 divisors, whose sum is σ = 528378942. Its totient is φ = 33369600.

The previous prime is 138085183. The next prime is 138085219. The reversal of 138085200 is 2580831.

It is a happy number.

138085200 is a `hidden beast` number, since 1 + 380 + 85 + 200 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 69696 + 138015504 = 264^2 + 11748^2 .

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 435442 + ... + 435758.

Almost surely, 2^138085200 is an apocalyptic number.

138085200 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 138085200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (264189471).

138085200 is an abundant number, since it is smaller than the sum of its proper divisors (390293742).

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

138085200 is a wasteful number, since it uses less digits than its factorization.

138085200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 363 (or 338 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 27.

The square root of 138085200 is about 11750.9659177448. The cubic root of 138085200 is about 516.8712520814.

The spelling of 138085200 in words is "one hundred thirty-eight million, eighty-five thousand, two hundred".