205772 has 12 divisors (see below), whose sum is σ = 411600. Its totient is φ = 88176.

The previous prime is 205763. The next prime is 205783. The reversal of 205772 is 277502.

205772 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

205772 is an admirable number.

It is an unprimeable number.

205772 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 3647 + ... + 3702.

It is an arithmetic number, because the mean of its divisors is an integer number (34300).

2²⁰⁵⁷⁷² is an apocalyptic number.

It is an amenable number.

205772 is a primitive abundant number, since it is smaller than the sum of its proper divisors, none of which is abundant.

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

205772 is a wasteful number, since it uses less digits than its factorization.

205772 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 7360 (or 7358 counting only the distinct ones).

The product of its (nonzero) digits is 980, while the sum is 23.

The square root of 205772 is about 453.6209871688. The cubic root of 205772 is about 59.0376088857.

It can be divided in two parts, 20 and 5772, that multiplied together give a triangular number (115440 = T₄₈₀).

The spelling of 205772 in words is "two hundred five thousand, seven hundred seventy-two".