204828800 has 216 divisors, whose sum is σ = 581404845. Its totient is φ = 71244800.

The previous prime is 204828779. The next prime is 204828803. The reversal of 204828800 is 8828402.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in 2 ways, for example, as 200732224 + 4096576 = 14168^2 + 2024^2 .

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=10120.

It is a Harshad number since it is a multiple of its sum of digits (32).

It is not an unprimeable number, because it can be changed into a prime (204828803) by changing a digit.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 8905589 + ... + 8905611.

Almost surely, 2^204828800 is an apocalyptic number.

204828800 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 204828800

204828800 is an abundant number, since it is smaller than the sum of its proper divisors (376576045).

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

204828800 is a wasteful number, since it uses less digits than its factorization.

204828800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 92 (or 41 counting only the distinct ones).

The product of its (nonzero) digits is 8192, while the sum is 32.

The square root of 204828800 is about 14311.8412512157. The cubic root of 204828800 is about 589.4726687236.

Multiplying 204828800 by its sum of digits (32), we get a square (6554521600 = 80960²).

204828800 divided by its sum of digits (32) gives a square (6400900 = 2530²).

Multiplying 204828800 by its product of nonzero digits (8192), we get a square (1677957529600 = 1295360²).

It can be divided in two parts, 2048 and 28800, that multiplied together give a square (58982400 = 7680²).

The spelling of 204828800 in words is "two hundred four million, eight hundred twenty-eight thousand, eight hundred".