138212728704000 has 2640 divisors, whose sum is σ = 552305233434240. Its totient is φ = 34364561817600.

The previous prime is 138212728703927. The next prime is 138212728704041. The reversal of 138212728704000 is 407827212831.

138212728704000 is a `hidden beast` number, since 1 + 3 + 8 + 212 + 7 + 28 + 7 + 0 + 400 + 0 = 666.

It is a hoax number, since the sum of its digits (45) 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 (45).

It is an unprimeable number.

It is a polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 578295935881 + ... + 578295936119.

It is an arithmetic number, because the mean of its divisors is an integer number (209206527816).

Almost surely, 2^{138212728704000} is an apocalyptic number.

138212728704000 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 138212728704000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (276152616717120).

138212728704000 is an abundant number, since it is smaller than the sum of its proper divisors (414092504730240).

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

138212728704000 is a wasteful number, since it uses less digits than its factorization.

138212728704000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 513 (or 459 counting only the distinct ones).

The product of its (nonzero) digits is 301056, while the sum is 45.

The spelling of 138212728704000 in words is "one hundred thirty-eight trillion, two hundred twelve billion, seven hundred twenty-eight million, seven hundred four thousand".