138657600 has 126 divisors (see below), whose sum is σ = 492873030. Its totient is φ = 36971520.

The previous prime is 138657581. The next prime is 138657619. The reversal of 138657600 is 6756831.

138657600 is a `hidden beast` number, since 1 + 3 + 86 + 576 + 0 + 0 = 666.

138657600 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (138657581) and next prime (138657619).

It can be written as a sum of positive squares in 3 ways, for example, as 43243776 + 95413824 = 6576^2 + 9768^2 .

It is a hoax number, since the sum of its digits (36) coincides with the sum of the digits of its distinct prime factors.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 9586 + ... + 19214.

Almost surely, 2^138657600 is an apocalyptic number.

138657600 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 138657600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (246436515).

138657600 is an abundant number, since it is smaller than the sum of its proper divisors (354215430).

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

138657600 is a wasteful number, since it uses less digits than its factorization.

138657600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 9657 (or 9639 counting only the distinct ones).

The product of its (nonzero) digits is 30240, while the sum is 36.

The square root of 138657600 is about 11775.2961746191. The cubic root of 138657600 is about 517.5844572651.

The spelling of 138657600 in words is "one hundred thirty-eight million, six hundred fifty-seven thousand, six hundred".