3968 has 16 divisors (see below), whose sum is σ = 8160. Its totient is φ = 1920.

The previous prime is 3967. The next prime is 3989. The reversal of 3968 is 8693.

It is a happy number.

It is a Cunningham number, because it is equal to 63²-1.

It is a tau number, because it is divible by the number of its divisors (16).

It is a plaindrome in base 5 and base 12.

It is a nialpdrome in base 2, base 4, base 8 and base 16.

It is a zygodrome in base 2 and base 5.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (3967) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 113 + ... + 143.

It is an arithmetic number, because the mean of its divisors is an integer number (510).

2³⁹⁶⁸ 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 3968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (4080).

3968 is an abundant number, since it is smaller than the sum of its proper divisors (4192).

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

3968 is an equidigital number, since it uses as much as digits as its factorization.

3968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 45 (or 33 counting only the distinct ones).

The product of its digits is 1296, while the sum is 26.

The square root of 3968 is about 62.9920629921. The cubic root of 3968 is about 15.8315664387.

It can be divided in two parts, 396 and 8, that added together give a palindrome (404).

The spelling of 3968 in words is "three thousand, nine hundred sixty-eight".