105684009600 has 768 divisors, whose sum is σ = 394374758400. Its totient is φ = 24695193600.

The previous prime is 105684009593. The next prime is 105684009623. The reversal of 105684009600 is 6900486501.

It is a super-2 number, since 2×105684009600² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (39).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 228258969 + ... + 228259431.

It is an arithmetic number, because the mean of its divisors is an integer number (513508800).

Almost surely, 2^105684009600 is an apocalyptic number.

105684009600 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 105684009600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (197187379200).

105684009600 is an abundant number, since it is smaller than the sum of its proper divisors (288690748800).

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

105684009600 is a wasteful number, since it uses less digits than its factorization.

105684009600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 593 (or 576 counting only the distinct ones).

The product of its (nonzero) digits is 51840, while the sum is 39.

The spelling of 105684009600 in words is "one hundred five billion, six hundred eighty-four million, nine thousand, six hundred".