10105935840 has 1920 divisors, whose sum is σ = 51636372480. Its totient is φ = 1791590400.

The previous prime is 10105935823. The next prime is 10105935887. The reversal of 10105935840 is 4853950101.

10105935840 is a `hidden beast` number, since 1 + 0 + 10 + 593 + 58 + 4 + 0 = 666.

10105935840 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a junction number, because it is equal to n+sod(n) for n = 10105935795 and 10105935804.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 319 ways as a sum of consecutive naturals, for example, 246486220 + ... + 246486260.

It is an arithmetic number, because the mean of its divisors is an integer number (26893944).

Almost surely, 2^10105935840 is an apocalyptic number.

10105935840 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 10105935840, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (25818186240).

10105935840 is an abundant number, since it is smaller than the sum of its proper divisors (41530436640).

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

10105935840 is a wasteful number, since it uses less digits than its factorization.

10105935840 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 118 (or 101 counting only the distinct ones).

The product of its (nonzero) digits is 21600, while the sum is 36.

The spelling of 10105935840 in words is "ten billion, one hundred five million, nine hundred thirty-five thousand, eight hundred forty".