7928668800 has 720 divisors, whose sum is σ = 31857355530. Its totient is φ = 1940889600.

The previous prime is 7928668799. The next prime is 7928668819. The reversal of 7928668800 is 88668297.

It can be written as a sum of positive squares in 9 ways, for example, as 1690196544 + 6238472256 = 41112^2 + 78984^2 .

It is a tau number, because it is divible by the number of its divisors (720).

It is a Smith number, since the sum of its digits (54) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a polite number, since it can be written in 89 ways as a sum of consecutive naturals, for example, 43804710 + ... + 43804890.

Almost surely, 2^7928668800 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7928668800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (15928677765).

7928668800 is an abundant number, since it is smaller than the sum of its proper divisors (23928686730).

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

7928668800 is a wasteful number, since it uses less digits than its factorization.

7928668800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 243 (or 204 counting only the distinct ones).

The product of its (nonzero) digits is 2322432, while the sum is 54.

The square root of 7928668800 is about 89043.0727232613. The cubic root of 7928668800 is about 1994.0379781414.

The spelling of 7928668800 in words is "seven billion, nine hundred twenty-eight million, six hundred sixty-eight thousand, eight hundred".