7968 has 24 divisors (see below), whose sum is σ = 21168. Its totient is φ = 2624.

The previous prime is 7963. The next prime is 7993. The reversal of 7968 is 8697.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (24).

It is a plaindrome in base 5.

It is a zygodrome in base 5.

It is not an unprimeable number, because it can be changed into a prime (7963) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 55 + ... + 137.

It is an arithmetic number, because the mean of its divisors is an integer number (882).

2⁷⁹⁶⁸ 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 7968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10584).

7968 is an abundant number, since it is smaller than the sum of its proper divisors (13200).

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

7968 is a wasteful number, since it uses less digits than its factorization.

7968 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 96 (or 88 counting only the distinct ones).

The product of its digits is 3024, while the sum is 30.

The square root of 7968 is about 89.2636544177. The cubic root of 7968 is about 19.9732976986.

Subtracting 7968 from its reverse (8697), we obtain a 6-th power (729 = 3⁶).

It can be divided in two parts, 7 and 968, that multiplied together give a palindrome (6776).

The spelling of 7968 in words is "seven thousand, nine hundred sixty-eight".