820382400 has 252 divisors, whose sum is σ = 3043836432. Its totient is φ = 209172480.

The previous prime is 820382393. The next prime is 820382411. The reversal of 820382400 is 4283028.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 329962 + ... + 332438.

It is an arithmetic number, because the mean of its divisors is an integer number (12078716).

Almost surely, 2^820382400 is an apocalyptic number.

820382400 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 820382400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1521918216).

820382400 is an abundant number, since it is smaller than the sum of its proper divisors (2223454032).

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

820382400 is a wasteful number, since it uses less digits than its factorization.

820382400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2528 (or 2510 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 27.

The square root of 820382400 is about 28642.3183419220. The cubic root of 820382400 is about 936.1356367102.

The spelling of 820382400 in words is "eight hundred twenty million, three hundred eighty-two thousand, four hundred".