105768000 has 336 divisors, whose sum is σ = 411059376. Its totient is φ = 25804800.

The previous prime is 105767989. The next prime is 105768031. The reversal of 105768000 is 867501.

105768000 is a `hidden beast` number, since 10 + 576 + 80 + 0 + 0 = 666.

It can be written as a sum of positive squares in 8 ways, for example, as 86266944 + 19501056 = 9288^2 + 4416^2 .

It is a super-2 number, since 2×105768000² = 22373739648000000, which contains 22 as substring.

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 47 ways as a sum of consecutive naturals, for example, 935944 + ... + 936056.

It is an arithmetic number, because the mean of its divisors is an integer number (1223391).

Almost surely, 2^105768000 is an apocalyptic number.

105768000 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 105768000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (205529688).

105768000 is an abundant number, since it is smaller than the sum of its proper divisors (305291376).

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

105768000 is a wasteful number, since it uses less digits than its factorization.

105768000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 159 (or 136 counting only the distinct ones).

The product of its (nonzero) digits is 1680, while the sum is 27.

The square root of 105768000 is about 10284.3570533116. The cubic root of 105768000 is about 472.9168237518.

The spelling of 105768000 in words is "one hundred five million, seven hundred sixty-eight thousand".