105768 has 48 divisors (see below), whose sum is σ = 311220. Its totient is φ = 32256.

The previous prime is 105767. The next prime is 105769. The reversal of 105768 is 867501.

It is an interprime number because it is at equal distance from previous prime (105767) and next prime (105769).

It can be written as a sum of positive squares in 2 ways, for example, as 79524 + 26244 = 282^2 + 162^2 .

It is a super-2 number, since 2×105768² = 22373739648, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (105761) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 880 + ... + 992.

2¹⁰⁵⁷⁶⁸ is an apocalyptic number.

105768 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 105768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (155610).

105768 is an abundant number, since it is smaller than the sum of its proper divisors (205452).

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

105768 is a wasteful number, since it uses less digits than its factorization.

105768 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 138 (or 131 counting only the distinct ones).

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

The square root of 105768 is about 325.2199255888. The cubic root of 105768 is about 47.2916823752.

It can be divided in two parts, 10 and 5768, that added together give a triangular number (5778 = T₁₀₇).

The spelling of 105768 in words is "one hundred five thousand, seven hundred sixty-eight".