823200 has 144 divisors (see below), whose sum is σ = 3124800. Its totient is φ = 188160.

The previous prime is 823183. The next prime is 823201. The reversal of 823200 is 2328.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a nialpdrome in base 7.

It is a zygodrome in base 7.

It is a self number, because there is not a number n which added to its sum of digits gives 823200.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 823200.

It is not an unprimeable number, because it can be changed into a prime (823201) by changing a digit.

823200 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, 117597 + ... + 117603.

It is an arithmetic number, because the mean of its divisors is an integer number (21700).

2⁸²³²⁰⁰ is an apocalyptic number.

823200 is a gapful number since it is divisible by the number (80) 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 823200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1562400).

823200 is an abundant number, since it is smaller than the sum of its proper divisors (2301600).

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

823200 is a wasteful number, since it uses less digits than its factorization.

823200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 44 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 15.

The square root of 823200 is about 907.3036977771. The cubic root of 823200 is about 93.7206130115.

Adding to 823200 its reverse (2328), we get a palindrome (825528).

The spelling of 823200 in words is "eight hundred twenty-three thousand, two hundred".