820400 has 60 divisors (see below), whose sum is σ = 2260272. Its totient is φ = 280320.

The previous prime is 820399. The next prime is 820409. The reversal of 820400 is 4028.

It is a Harshad number since it is a multiple of its sum of digits (14).

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 820400.

It is not an unprimeable number, because it can be changed into a prime (820409) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2654 + ... + 2946.

2⁸²⁰⁴⁰⁰ is an apocalyptic number.

820400 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 820400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1130136).

820400 is an abundant number, since it is smaller than the sum of its proper divisors (1439872).

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

820400 is a wasteful number, since it uses less digits than its factorization.

820400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 318 (or 307 counting only the distinct ones).

The product of its (nonzero) digits is 64, while the sum is 14.

The square root of 820400 is about 905.7593499379. The cubic root of 820400 is about 93.6142331096.

Adding to 820400 its reverse (4028), we get a palindrome (824428).

The spelling of 820400 in words is "eight hundred twenty thousand, four hundred".