8199734400 has 864 divisors, whose sum is σ = 34825414260. Its totient is φ = 1824768000.

The previous prime is 8199734399. The next prime is 8199734429. The reversal of 8199734400 is 44379918.

It can be written as a sum of positive squares in 6 ways, for example, as 95413824 + 8104320576 = 9768^2 + 90024^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

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 107 ways as a sum of consecutive naturals, for example, 45302310 + ... + 45302490.

Almost surely, 2^8199734400 is an apocalyptic number.

8199734400 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 8199734400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17412707130).

8199734400 is an abundant number, since it is smaller than the sum of its proper divisors (26625679860).

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

8199734400 is a wasteful number, since it uses less digits than its factorization.

8199734400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 246 (or 215 counting only the distinct ones).

The product of its (nonzero) digits is 217728, while the sum is 45.

The square root of 8199734400 is about 90552.3848388324. The cubic root of 8199734400 is about 2016.5079030204.

The spelling of 8199734400 in words is "eight billion, one hundred ninety-nine million, seven hundred thirty-four thousand, four hundred".