105979305600 has 1152 divisors, whose sum is σ = 463478371200. Its totient is φ = 22585835520.

The previous prime is 105979305581. The next prime is 105979305659. The reversal of 105979305600 is 6503979501.

105979305600 is a `hidden beast` number, since 1 + 0 + 5 + 9 + 7 + 9 + 30 + 5 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

It is a super-2 number, since 2×105979305600² (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 pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 990460747 + ... + 990460853.

It is an arithmetic number, because the mean of its divisors is an integer number (402324975).

Almost surely, 2^105979305600 is an apocalyptic number.

105979305600 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 105979305600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (231739185600).

105979305600 is an abundant number, since it is smaller than the sum of its proper divisors (357499065600).

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

105979305600 is a wasteful number, since it uses less digits than its factorization.

105979305600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 195 (or 141 counting only the distinct ones).

The product of its (nonzero) digits is 255150, while the sum is 45.

The spelling of 105979305600 in words is "one hundred five billion, nine hundred seventy-nine million, three hundred five thousand, six hundred".