820814400 has 504 divisors, whose sum is σ = 3537630720. Its totient is φ = 176209920.

The previous prime is 820814399. The next prime is 820814411. The reversal of 820814400 is 4418028.

820814400 = T₇₇₈₄ + T₇₇₈₅ + ... + T₇₈₁₀.

It is a tau number, because it is divible by the number of its divisors (504).

It is a congruent number.

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 71 ways as a sum of consecutive naturals, for example, 1713361 + ... + 1713839.

Almost surely, 2^820814400 is an apocalyptic number.

820814400 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 820814400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1768815360).

820814400 is an abundant number, since it is smaller than the sum of its proper divisors (2716816320).

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

820814400 is a wasteful number, since it uses less digits than its factorization.

820814400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 531 (or 513 counting only the distinct ones).

The product of its (nonzero) digits is 2048, while the sum is 27.

The square root of 820814400 is about 28649.8586383947. The cubic root of 820814400 is about 936.2999257989.

The spelling of 820814400 in words is "eight hundred twenty million, eight hundred fourteen thousand, four hundred".