10585384992 has 768 divisors, whose sum is σ = 40534179840. Its totient is φ = 2612736000.

The previous prime is 10585384973. The next prime is 10585384993. The reversal of 10585384992 is 29948358501.

10585384992 is a `hidden beast` number, since 10 + 5 + 8 + 538 + 4 + 9 + 92 = 666.

It is a super-2 number, since 2×10585384992² (a number of 21 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is not an unprimeable number, because it can be changed into a prime (10585384993) by changing a digit.

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 127 ways as a sum of consecutive naturals, for example, 104805742 + ... + 104805842.

It is an arithmetic number, because the mean of its divisors is an integer number (52778880).

Almost surely, 2^10585384992 is an apocalyptic number.

10585384992 is a gapful number since it is divisible by the number (12) 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 10585384992, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (20267089920).

10585384992 is an abundant number, since it is smaller than the sum of its proper divisors (29948794848).

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

10585384992 is a wasteful number, since it uses less digits than its factorization.

10585384992 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 214 (or 200 counting only the distinct ones).

The product of its (nonzero) digits is 3110400, while the sum is 54.

The spelling of 10585384992 in words is "ten billion, five hundred eighty-five million, three hundred eighty-four thousand, nine hundred ninety-two".