105385370688 has 168 divisors, whose sum is σ = 326055329600. Its totient is φ = 32351394816.

The previous prime is 105385370641. The next prime is 105385370707. The reversal of 105385370688 is 886073583501.

105385370688 is a `hidden beast` number, since 10 + 5 + 38 + 537 + 0 + 68 + 8 = 666.

It is a super-2 number, since 2×105385370688² (a number of 23 digits) contains 22 as substring.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 3271203 + ... + 3303261.

Almost surely, 2^105385370688 is an apocalyptic number.

105385370688 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 105385370688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (163027664800).

105385370688 is an abundant number, since it is smaller than the sum of its proper divisors (220669958912).

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

105385370688 is a wasteful number, since it uses less digits than its factorization.

105385370688 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 32529 (or 32516 counting only the distinct ones).

The product of its (nonzero) digits is 4838400, while the sum is 54.

The spelling of 105385370688 in words is "one hundred five billion, three hundred eighty-five million, three hundred seventy thousand, six hundred eighty-eight".