820582400 has 288 divisors, whose sum is σ = 2339850240. Its totient is φ = 282624000.

The previous prime is 820582381. The next prime is 820582409. The reversal of 820582400 is 4285028.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (820582409) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 17459177 + ... + 17459223.

It is an arithmetic number, because the mean of its divisors is an integer number (8124480).

Almost surely, 2^820582400 is an apocalyptic number.

820582400 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 820582400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1169925120).

820582400 is an abundant number, since it is smaller than the sum of its proper divisors (1519267840).

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

820582400 is a wasteful number, since it uses less digits than its factorization.

820582400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 121 (or 96 counting only the distinct ones).

The product of its (nonzero) digits is 5120, while the sum is 29.

The square root of 820582400 is about 28645.8094666567. The cubic root of 820582400 is about 936.2117036414.

The spelling of 820582400 in words is "eight hundred twenty million, five hundred eighty-two thousand, four hundred".