9968 has 20 divisors (see below), whose sum is σ = 22320. Its totient is φ = 4224.

The previous prime is 9967. The next prime is 9973. The reversal of 9968 is 8699.

9968 = T₂₇ + T₂₈ + ... + T₄₂.

It is a happy number.

9968 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a super-2 number, since 2×9968² = 198722048, which contains 22 as substring.

It is a Smith number, since the sum of its digits (32) coincides with the sum of the digits of its prime factors.

It is a nialpdrome in base 11.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (9967) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 68 + ... + 156.

It is an arithmetic number, because the mean of its divisors is an integer number (1116).

2⁹⁹⁶⁸ 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 9968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (11160).

9968 is an abundant number, since it is smaller than the sum of its proper divisors (12352).

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

9968 is a wasteful number, since it uses less digits than its factorization.

9968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 104 (or 98 counting only the distinct ones).

The product of its digits is 3888, while the sum is 32.

The square root of 9968 is about 99.8398717948. The cubic root of 9968 is about 21.5213417073.

Adding to 9968 its sum of digits (32), we get a 4-th power (10000 = 10⁴).

The spelling of 9968 in words is "nine thousand, nine hundred sixty-eight".