205200 has 120 divisors (see below), whose sum is σ = 768800. Its totient is φ = 51840.

The previous prime is 205187. The next prime is 205201. The reversal of 205200 is 2502.

205200 = 15³ + 16³ + ... + 30³.

It is a tau number, because it is divible by the number of its divisors (120).

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a nialpdrome in base 6.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 205200.

It is not an unprimeable number, because it can be changed into a prime (205201) by changing a digit.

205200 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 10791 + ... + 10809.

2²⁰⁵²⁰⁰ is an apocalyptic number.

205200 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 205200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (384400).

205200 is an abundant number, since it is smaller than the sum of its proper divisors (563600).

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

205200 is a wasteful number, since it uses less digits than its factorization.

205200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 46 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 20, while the sum is 9.

The square root of 205200 is about 452.9900661162. The cubic root of 205200 is about 58.9828543495.

Adding to 205200 its reverse (2502), we get a palindrome (207702).

The spelling of 205200 in words is "two hundred five thousand, two hundred".