820688400 has 360 divisors, whose sum is σ = 3370111680. Its totient is φ = 180956160.

The previous prime is 820688353. The next prime is 820688417. The reversal of 820688400 is 4886028.

It is a tau number, because it is divible by the number of its divisors (360).

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 730239 + ... + 731361.

Almost surely, 2^820688400 is an apocalyptic number.

820688400 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 820688400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1685055840).

820688400 is an abundant number, since it is smaller than the sum of its proper divisors (2549423280).

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

820688400 is a wasteful number, since it uses less digits than its factorization.

820688400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1183 (or 1169 counting only the distinct ones).

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

The square root of 820688400 is about 28647.6595902702. The cubic root of 820688400 is about 936.2520141038.

The spelling of 820688400 in words is "eight hundred twenty million, six hundred eighty-eight thousand, four hundred".