205728432000 has 768 divisors, whose sum is σ = 844216888320. Its totient is φ = 43394457600.

The previous prime is 205728431983. The next prime is 205728432001. The reversal of 205728432000 is 234827502.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (205728432001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 56782189 + ... + 56785811.

It is an arithmetic number, because the mean of its divisors is an integer number (1099240740).

Almost surely, 2^205728432000 is an apocalyptic number.

205728432000 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 205728432000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (422108444160).

205728432000 is an abundant number, since it is smaller than the sum of its proper divisors (638488456320).

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

205728432000 is a wasteful number, since it uses less digits than its factorization.

205728432000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3688 (or 3653 counting only the distinct ones).

The product of its (nonzero) digits is 26880, while the sum is 33.

The spelling of 205728432000 in words is "two hundred five billion, seven hundred twenty-eight million, four hundred thirty-two thousand".