105972 has 12 divisors (see below), whose sum is σ = 247296. Its totient is φ = 35320.

The previous prime is 105971. The next prime is 105977. The reversal of 105972 is 279501.

It is a tau number, because it is divible by the number of its divisors (12).

It is a super-2 number, since 2×105972² = 22460129568, which contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (105971) by changing a digit.

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 3 ways as a sum of consecutive naturals, for example, 4404 + ... + 4427.

It is an arithmetic number, because the mean of its divisors is an integer number (20608).

2¹⁰⁵⁹⁷² is an apocalyptic number.

105972 is a gapful number since it is divisible by the number (12) formed by its first and last digit.

It is an amenable number.

105972 is an abundant number, since it is smaller than the sum of its proper divisors (141324).

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

105972 is a wasteful number, since it uses less digits than its factorization.

105972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 8838 (or 8836 counting only the distinct ones).

The product of its (nonzero) digits is 630, while the sum is 24.

The square root of 105972 is about 325.5334084238. The cubic root of 105972 is about 47.3220674548.

The spelling of 105972 in words is "one hundred five thousand, nine hundred seventy-two".