8209812800 has 126 divisors (see below), whose sum is σ = 23499661662. Its totient is φ = 2814766080.

The previous prime is 8209812769. The next prime is 8209812811. The reversal of 8209812800 is 82189028.

It can be written as a sum of positive squares in 3 ways, for example, as 3136 + 8209809664 = 56^2 + 90608^2 .

It is a super-2 number, since 2×8209812800² (a number of 21 digits) contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 26042 + ... + 130758.

Almost surely, 2^8209812800 is an apocalyptic number.

8209812800 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 8209812800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (11749830831).

8209812800 is an abundant number, since it is smaller than the sum of its proper divisors (15289848862).

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

8209812800 is a wasteful number, since it uses less digits than its factorization.

8209812800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 104753 (or 104731 counting only the distinct ones).

The product of its (nonzero) digits is 18432, while the sum is 38.

The square root of 8209812800 is about 90608.0173053136. The cubic root of 8209812800 is about 2017.3337367790. Note that the first 3 decimals are identical.

The spelling of 8209812800 in words is "eight billion, two hundred nine million, eight hundred twelve thousand, eight hundred".