205752960 has 432 divisors, whose sum is σ = 858233610. Its totient is φ = 47029248.

The previous prime is 205752931. The next prime is 205752961. The reversal of 205752960 is 69257502.

205752960 is a `hidden beast` number, since 2 + 0 + 575 + 29 + 60 = 666.

It can be written as a sum of positive squares in only one way, i.e., 185177664 + 20575296 = 13608^2 + 4536^2 .

It is a tau number, because it is divible by the number of its divisors (432).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (205752961) by changing a digit.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 29393277 + ... + 29393283.

Almost surely, 2^205752960 is an apocalyptic number.

205752960 is a gapful number since it is divisible by the number (20) 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 205752960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (429116805).

205752960 is an abundant number, since it is smaller than the sum of its proper divisors (652480650).

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

205752960 is an frugal number, since it uses more digits than its factorization.

205752960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 57 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 37800, while the sum is 36.

The square root of 205752960 is about 14344.0914665238. The cubic root of 205752960 is about 590.3578792080.

The spelling of 205752960 in words is "two hundred five million, seven hundred fifty-two thousand, nine hundred sixty".