205049408800 has 72 divisors (see below), whose sum is σ = 500867793972. Its totient is φ = 81972096000.

The previous prime is 205049408783. The next prime is 205049408819. The reversal of 205049408800 is 8804940502.

205049408800 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 6 ways, for example, as 19657161616 + 185392247184 = 140204^2 + 430572^2 .

It is a Harshad number since it is a multiple of its sum of digits (40).

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1319190 + ... + 1466410.

Almost surely, 2^205049408800 is an apocalyptic number.

205049408800 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 205049408800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (250433896986).

205049408800 is an abundant number, since it is smaller than the sum of its proper divisors (295818385172).

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

205049408800 is a wasteful number, since it uses less digits than its factorization.

205049408800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 148982 (or 148969 counting only the distinct ones).

The product of its (nonzero) digits is 92160, while the sum is 40.

The spelling of 205049408800 in words is "two hundred five billion, forty-nine million, four hundred eight thousand, eight hundred".