1008820800 has 504 divisors, whose sum is σ = 4101440616. Its totient is φ = 232980480.

The previous prime is 1008820793. The next prime is 1008820801. The reversal of 1008820800 is 80288001.

It can be written as a sum of positive squares in 12 ways, for example, as 574848576 + 433972224 = 23976^2 + 20832^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1008820801) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 3182242 + ... + 3182558.

It is an arithmetic number, because the mean of its divisors is an integer number (8137779).

Almost surely, 2^1008820800 is an apocalyptic number.

1008820800 is a gapful number since it is divisible by the number (10) 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 1008820800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2050720308).

1008820800 is an abundant number, since it is smaller than the sum of its proper divisors (3092619816).

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

1008820800 is a wasteful number, since it uses less digits than its factorization.

1008820800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 375 (or 357 counting only the distinct ones).

The product of its (nonzero) digits is 1024, while the sum is 27.

The square root of 1008820800 is about 31761.9394873802. The cubic root of 1008820800 is about 1002.9316636162.

It can be divided in two parts, 100 and 8820800, that added together give a square (8820900 = 2970²).

The spelling of 1008820800 in words is "one billion, eight million, eight hundred twenty thousand, eight hundred".