138624640000 has 880 divisors, whose sum is σ = 451219063680. Its totient is φ = 41287680000.

The previous prime is 138624639997. The next prime is 138624640043. The reversal of 138624640000 is 46426831.

It is a tau number, because it is divible by the number of its divisors (880).

It is an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 1429119952 + ... + 1429120048.

It is an arithmetic number, because the mean of its divisors is an integer number (512748936).

Almost surely, 2^138624640000 is an apocalyptic number.

138624640000 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 138624640000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (225609531840).

138624640000 is an abundant number, since it is smaller than the sum of its proper divisors (312594423680).

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

138624640000 is an equidigital number, since it uses as much as digits as its factorization.

138624640000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 184 (or 151 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 34.

It can be divided in two parts, 1386 and 24640000, that multiplied together give a square (34151040000 = 184800²).

The spelling of 138624640000 in words is "one hundred thirty-eight billion, six hundred twenty-four million, six hundred forty thousand".