138315313920 has 576 divisors, whose sum is σ = 525641711616. Its totient is φ = 30330961920.

The previous prime is 138315313891. The next prime is 138315313991. The reversal of 138315313920 is 29313513831.

138315313920 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a super-2 number, since 2×138315313920² (a number of 23 digits) contains 22 as substring.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 105825907 + ... + 105827213.

It is an arithmetic number, because the mean of its divisors is an integer number (912572416).

Almost surely, 2^138315313920 is an apocalyptic number.

138315313920 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 138315313920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (262820855808).

138315313920 is an abundant number, since it is smaller than the sum of its proper divisors (387326397696).

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

138315313920 is a wasteful number, since it uses less digits than its factorization.

138315313920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1496 (or 1482 counting only the distinct ones).

The product of its (nonzero) digits is 58320, while the sum is 39.

The spelling of 138315313920 in words is "one hundred thirty-eight billion, three hundred fifteen million, three hundred thirteen thousand, nine hundred twenty".