284800 has 48 divisors (see below), whose sum is σ = 711450. Its totient is φ = 112640.

The previous prime is 284783. The next prime is 284803. The reversal of 284800 is 8482.

It can be written as a sum of positive squares in 3 ways, for example, as 166464 + 118336 = 408^2 + 344^2 .

It is a super-2 number, since 2×284800² = 162222080000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (284803) by changing a digit.

284800 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 3156 + ... + 3244.

2²⁸⁴⁸⁰⁰ is an apocalyptic number.

284800 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 284800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (355725).

284800 is an abundant number, since it is smaller than the sum of its proper divisors (426650).

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

284800 is an equidigital number, since it uses as much as digits as its factorization.

284800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 113 (or 96 counting only the distinct ones).

The product of its (nonzero) digits is 512, while the sum is 22.

The square root of 284800 is about 533.6665625651. Note that the first 3 decimals coincide. The cubic root of 284800 is about 65.7930462621.

The spelling of 284800 in words is "two hundred eighty-four thousand, eight hundred".