810400 has 36 divisors (see below), whose sum is σ = 1980342. Its totient is φ = 323840.

The previous prime is 810391. The next prime is 810401. The reversal of 810400 is 4018.

It can be written as a sum of positive squares in 3 ways, for example, as 309136 + 501264 = 556^2 + 708^2 .

It is not an unprimeable number, because it can be changed into a prime (810401) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 294 + ... + 1306.

2⁸¹⁰⁴⁰⁰ is an apocalyptic number.

810400 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 810400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (990171).

810400 is an abundant number, since it is smaller than the sum of its proper divisors (1169942).

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

810400 is a wasteful number, since it uses less digits than its factorization.

810400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1033 (or 1020 counting only the distinct ones).

The product of its (nonzero) digits is 32, while the sum is 13.

The square root of 810400 is about 900.2221947942. Note that the first 3 decimals coincide. The cubic root of 810400 is about 93.2323170115.

Adding to 810400 its reverse (4018), we get a palindrome (814418).

The spelling of 810400 in words is "eight hundred ten thousand, four hundred".