138189600 has 216 divisors, whose sum is σ = 516412260. Its totient is φ = 34652160.

The previous prime is 138189581. The next prime is 138189619. The reversal of 138189600 is 6981831.

138189600 is a `hidden beast` number, since 1 + 38 + 18 + 9 + 600 = 666.

It is an interprime number because it is at equal distance from previous prime (138189581) and next prime (138189619).

It can be written as a sum of positive squares in 6 ways, for example, as 37307664 + 100881936 = 6108^2 + 10044^2 .

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 121836 + ... + 122964.

Almost surely, 2^138189600 is an apocalyptic number.

138189600 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 138189600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (258206130).

138189600 is an abundant number, since it is smaller than the sum of its proper divisors (378222660).

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

138189600 is a wasteful number, since it uses less digits than its factorization.

138189600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1172 (or 1156 counting only the distinct ones).

The product of its (nonzero) digits is 10368, while the sum is 36.

The square root of 138189600 is about 11755.4072664455. The cubic root of 138189600 is about 517.0014802911.

The spelling of 138189600 in words is "one hundred thirty-eight million, one hundred eighty-nine thousand, six hundred".