33968 has 20 divisors (see below), whose sum is σ = 72168. Its totient is φ = 15360.

The previous prime is 33967. The next prime is 33997. The reversal of 33968 is 86933.

33968 = T₅₇ + T₅₈ + ... + T₇₂.

It is a plaindrome in base 13.

It is a nialpdrome in base 14.

It is a self number, because there is not a number n which added to its sum of digits gives 33968.

It is not an unprimeable number, because it can be changed into a prime (33961) 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 in 3 ways as a sum of consecutive naturals, for example, 80 + ... + 272.

2³³⁹⁶⁸ 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 33968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (36084).

33968 is an abundant number, since it is smaller than the sum of its proper divisors (38200).

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

33968 is a wasteful number, since it uses less digits than its factorization.

33968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 212 (or 206 counting only the distinct ones).

The product of its digits is 3888, while the sum is 29.

The square root of 33968 is about 184.3040965361. The cubic root of 33968 is about 32.3859513346.

It can be divided in two parts, 33 and 968, that added together give a palindrome (1001).

The spelling of 33968 in words is "thirty-three thousand, nine hundred sixty-eight".