820684800 has 432 divisors, whose sum is σ = 3188350620. Its totient is φ = 200540160.

The previous prime is 820684769. The next prime is 820684817. The reversal of 820684800 is 8486028.

It can be written as a sum of positive squares in 6 ways, for example, as 183223296 + 637461504 = 13536^2 + 25248^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 5990332 + ... + 5990468.

Almost surely, 2^820684800 is an apocalyptic number.

820684800 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 820684800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1594175310).

820684800 is an abundant number, since it is smaller than the sum of its proper divisors (2367665820).

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

820684800 is a wasteful number, since it uses less digits than its factorization.

820684800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 188 (or 160 counting only the distinct ones).

The product of its (nonzero) digits is 24576, while the sum is 36.

The square root of 820684800 is about 28647.5967578434. The cubic root of 820684800 is about 936.2506451262.

It can be divided in two parts, 82068 and 4800, that added together give a palindrome (86868).

The spelling of 820684800 in words is "eight hundred twenty million, six hundred eighty-four thousand, eight hundred".