205752960000 has 1485 divisors, whose sum is σ = 896773908459. Its totient is φ = 47029248000.

The previous prime is 205752959963. The next prime is 205752960011. The reversal of 205752960000 is 69257502.

The square root of 205752960000 is 453600.

It is a perfect power (a square), and thus also a powerful number.

205752960000 is a `hidden beast` number, since 2 + 0 + 575 + 29 + 60 + 0 + 0 + 0 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 16131032064 + 189621927936 = 127008^2 + 435456^2 .

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 134 ways as a sum of consecutive naturals, for example, 29393279997 + ... + 29393280003.

Almost surely, 2^205752960000 is an apocalyptic number.

205752960000 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

205752960000 is the 453600-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 205752960000

205752960000 is an abundant number, since it is smaller than the sum of its proper divisors (691020948459).

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

205752960000 is an frugal number, since it uses more digits than its factorization.

205752960000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 78 (or 17 counting only the distinct ones).

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

Multiplying 205752960000 by its sum of digits (36), we get a square (7407106560000 = 2721600²).

205752960000 divided by its sum of digits (36) gives a square (5715360000 = 75600²).

The spelling of 205752960000 in words is "two hundred five billion, seven hundred fifty-two million, nine hundred sixty thousand".