7728 has 40 divisors (see below), whose sum is σ = 23808. Its totient is φ = 2112.

The previous prime is 7727. The next prime is 7741. The reversal of 7728 is 8277.

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

It is a nude number because it is divisible by every one of its digits.

It is a nialpdrome in base 6.

It is a zygodrome in base 2.

It is a junction number, because it is equal to n+sod(n) for n = 7698 and 7707.

It is not an unprimeable number, because it can be changed into a prime (7723) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 325 + ... + 347.

2⁷⁷²⁸ 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 7728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (11904).

7728 is an abundant number, since it is smaller than the sum of its proper divisors (16080).

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

7728 is a wasteful number, since it uses less digits than its factorization.

7728 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 41 (or 35 counting only the distinct ones).

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

The square root of 7728 is about 87.9090439033. The cubic root of 7728 is about 19.7707147930.

It can be divided in two parts, 772 and 8, that added together give a triangular number (780 = T₃₉).

The spelling of 7728 in words is "seven thousand, seven hundred twenty-eight".