105992409600 has 1440 divisors, whose sum is σ = 494570577600. Its totient is φ = 21985689600.

The previous prime is 105992409533. The next prime is 105992409613. The reversal of 105992409600 is 6904299501.

105992409600 is a `hidden beast` number, since 10 + 5 + 9 + 9 + 24 + 0 + 9 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (1440).

It is a super-2 number, since 2×105992409600² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 186278116 + ... + 186278684.

It is an arithmetic number, because the mean of its divisors is an integer number (343451790).

Almost surely, 2^105992409600 is an apocalyptic number.

105992409600 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 105992409600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (247285288800).

105992409600 is an abundant number, since it is smaller than the sum of its proper divisors (388578168000).

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

105992409600 is a wasteful number, since it uses less digits than its factorization.

105992409600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 631 (or 597 counting only the distinct ones).

The product of its (nonzero) digits is 174960, while the sum is 45.

The spelling of 105992409600 in words is "one hundred five billion, nine hundred ninety-two million, four hundred nine thousand, six hundred".