138153600 has 480 divisors, whose sum is σ = 562424940. Its totient is φ = 33177600.

The previous prime is 138153599. The next prime is 138153601. The reversal of 138153600 is 6351831.

138153600 is a `hidden beast` number, since 1 + 3 + 8 + 1 + 53 + 600 = 666.

It is an interprime number because it is at equal distance from previous prime (138153599) and next prime (138153601).

It can be written as a sum of positive squares in 6 ways, for example, as 3779136 + 134374464 = 1944^2 + 11592^2 .

It is a tau number, because it is divible by the number of its divisors (480).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (138153601) by changing a digit.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 3369580 + ... + 3369620.

Almost surely, 2^138153600 is an apocalyptic number.

138153600 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 138153600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (281212470).

138153600 is an abundant number, since it is smaller than the sum of its proper divisors (424271340).

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

138153600 is a wasteful number, since it uses less digits than its factorization.

138153600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 90 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 2160, while the sum is 27.

The square root of 138153600 is about 11753.8759564664. The cubic root of 138153600 is about 516.9565814233.

The spelling of 138153600 in words is "one hundred thirty-eight million, one hundred fifty-three thousand, six hundred".