4205728800 has 864 divisors, whose sum is σ = 18767548800. Its totient is φ = 880588800.

The previous prime is 4205728789. The next prime is 4205728819. The reversal of 4205728800 is 88275024.

It is a happy number.

4205728800 is a `hidden beast` number, since 4 + 2 + 0 + 572 + 8 + 80 + 0 = 666.

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

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 32104735 + ... + 32104865.

It is an arithmetic number, because the mean of its divisors is an integer number (21721700).

Almost surely, 2^4205728800 is an apocalyptic number.

4205728800 is a gapful number since it is divisible by the number (40) 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 4205728800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (9383774400).

4205728800 is an abundant number, since it is smaller than the sum of its proper divisors (14561820000).

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

4205728800 is a wasteful number, since it uses less digits than its factorization.

4205728800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 191 (or 161 counting only the distinct ones).

The product of its (nonzero) digits is 35840, while the sum is 36.

The square root of 4205728800 is about 64851.5905741717. The cubic root of 4205728800 is about 1614.1618849706.

The spelling of 4205728800 in words is "four billion, two hundred five million, seven hundred twenty-eight thousand, eight hundred".