105709968 has 160 divisors (see below), whose sum is σ = 373587200. Its totient is φ = 27869184.

The previous prime is 105709963. The next prime is 105709991. The reversal of 105709968 is 869907501.

105709968 is a `hidden beast` number, since 10 + 570 + 9 + 9 + 68 = 666.

It is a super-2 number, since 2×105709968² = 22349194669122048, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (105709963) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 37968 + ... + 40656.

It is an arithmetic number, because the mean of its divisors is an integer number (2334920).

Almost surely, 2^105709968 is an apocalyptic number.

105709968 is a gapful number since it is divisible by the number (18) 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 105709968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (186793600).

105709968 is an abundant number, since it is smaller than the sum of its proper divisors (267877232).

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

105709968 is a wasteful number, since it uses less digits than its factorization.

105709968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2726 (or 2714 counting only the distinct ones).

The product of its (nonzero) digits is 136080, while the sum is 45.

The square root of 105709968 is about 10281.5352939140. The cubic root of 105709968 is about 472.8303157659.

The spelling of 105709968 in words is "one hundred five million, seven hundred nine thousand, nine hundred sixty-eight".