33768 has 48 divisors (see below), whose sum is σ = 106080. Its totient is φ = 9504.

The previous prime is 33767. The next prime is 33769. The reversal of 33768 is 86733.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (33767) and next prime (33769).

It is a super-2 number, since 2×33768² = 2280555648, which contains 22 as substring.

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

It is a nialpdrome in base 14.

It is not an unprimeable number, because it can be changed into a prime (33767) 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 11 ways as a sum of consecutive naturals, for example, 471 + ... + 537.

It is an arithmetic number, because the mean of its divisors is an integer number (2210).

2³³⁷⁶⁸ 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 33768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (53040).

33768 is an abundant number, since it is smaller than the sum of its proper divisors (72312).

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

33768 is a wasteful number, since it uses less digits than its factorization.

33768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 86 (or 79 counting only the distinct ones).

The product of its digits is 3024, while the sum is 27.

The square root of 33768 is about 183.7607139734. The cubic root of 33768 is about 32.3222644886.

The spelling of 33768 in words is "thirty-three thousand, seven hundred sixty-eight".