138933384408000 has 5040 divisors, whose sum is σ = 685957339308384. Its totient is φ = 27570983731200.

The previous prime is 138933384407989. The next prime is 138933384408047. The reversal of 138933384408000 is 804483339831.

138933384408000 is a `hidden beast` number, since 1 + 3 + 8 + 93 + 3 + 38 + 440 + 80 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (5040).

It is a super-3 number, since 3×138933384408000³ (a number of 43 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 719 ways as a sum of consecutive naturals, for example, 91223495239 + ... + 91223496761.

Almost surely, 2^{138933384408000} is an apocalyptic number.

138933384408000 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 138933384408000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (342978669654192).

138933384408000 is an abundant number, since it is smaller than the sum of its proper divisors (547023954900384).

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

138933384408000 is a wasteful number, since it uses less digits than its factorization.

138933384408000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1619 (or 1570 counting only the distinct ones).

The product of its (nonzero) digits is 5971968, while the sum is 54.

The spelling of 138933384408000 in words is "one hundred thirty-eight trillion, nine hundred thirty-three billion, three hundred eighty-four million, four hundred eight thousand".