138120991656768 has 1344 divisors, whose sum is σ = 475080876933120. Its totient is φ = 39134222696448.

The previous prime is 138120991656667. The next prime is 138120991656799. The reversal of 138120991656768 is 867656199021831.

138120991656768 is a `hidden beast` number, since 1 + 38 + 1 + 20 + 9 + 9 + 1 + 6 + 567 + 6 + 8 = 666.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is a junction number, because it is equal to n+sod(n) for n = 138120991656696 and 138120991656705.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 89514575805 + ... + 89514577347.

Almost surely, 2^{138120991656768} is an apocalyptic number.

138120991656768 is a gapful number since it is divisible by the number (18) 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 138120991656768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (237540438466560).

138120991656768 is an abundant number, since it is smaller than the sum of its proper divisors (336959885276352).

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

138120991656768 is a wasteful number, since it uses less digits than its factorization.

138120991656768 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2009 (or 1974 counting only the distinct ones).

The product of its (nonzero) digits is 235146240, while the sum is 72.

The spelling of 138120991656768 in words is "one hundred thirty-eight trillion, one hundred twenty billion, nine hundred ninety-one million, six hundred fifty-six thousand, seven hundred sixty-eight".