105509496960 has 864 divisors, whose sum is σ = 439059617100. Its totient is φ = 23278510080.

The previous prime is 105509496941. The next prime is 105509496971. The reversal of 105509496960 is 69694905501.

105509496960 is a `hidden beast` number, since 1 + 0 + 5 + 509 + 49 + 6 + 96 + 0 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 100925665344 + 4583831616 = 317688^2 + 67704^2 .

It is a super-2 number, since 2×105509496960² (a number of 23 digits) contains 22 as substring.

It is a junction number, because it is equal to n+sod(n) for n = 105509496897 and 105509496906.

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 107 ways as a sum of consecutive naturals, for example, 271232446 + ... + 271232834.

Almost surely, 2^105509496960 is an apocalyptic number.

105509496960 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 105509496960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (219529808550).

105509496960 is an abundant number, since it is smaller than the sum of its proper divisors (333550120140).

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

105509496960 is a wasteful number, since it uses less digits than its factorization.

105509496960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 490 (or 437 counting only the distinct ones).

The product of its (nonzero) digits is 2624400, while the sum is 54.

The spelling of 105509496960 in words is "one hundred five billion, five hundred nine million, four hundred ninety-six thousand, nine hundred sixty".