138564000 has 192 divisors, whose sum is σ = 504766080. Its totient is φ = 36921600.

The previous prime is 138563981. The next prime is 138564031. The reversal of 138564000 is 465831.

138564000 is a `hidden beast` number, since 13 + 8 + 5 + 640 + 0 + 0 = 666.

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

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 107359 + ... + 108641.

It is an arithmetic number, because the mean of its divisors is an integer number (2628990).

Almost surely, 2^138564000 is an apocalyptic number.

138564000 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 138564000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (252383040).

138564000 is an abundant number, since it is smaller than the sum of its proper divisors (366202080).

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

138564000 is a wasteful number, since it uses less digits than its factorization.

138564000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1317 (or 1293 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

The square root of 138564000 is about 11771.3210813400. The cubic root of 138564000 is about 517.4679669313.

The spelling of 138564000 in words is "one hundred thirty-eight million, five hundred sixty-four thousand".