7728000 has 256 divisors, whose sum is σ = 30551040. Its totient is φ = 1689600.

The previous prime is 7727989. The next prime is 7728031. The reversal of 7728000 is 8277.

7728000 is digitally balanced in base 4, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 335989 + ... + 336011.

It is an arithmetic number, because the mean of its divisors is an integer number (119340).

Almost surely, 2^7728000 is an apocalyptic number.

7728000 is a gapful number since it is divisible by the number (70) 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 7728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (15275520).

7728000 is an abundant number, since it is smaller than the sum of its proper divisors (22823040).

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

7728000 is a wasteful number, since it uses less digits than its factorization.

7728000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 62 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 784, while the sum is 24.

The square root of 7728000 is about 2779.9280566230. The cubic root of 7728000 is about 197.7071479295.

The spelling of 7728000 in words is "seven million, seven hundred twenty-eight thousand".