33680 has 20 divisors (see below), whose sum is σ = 78492. Its totient is φ = 13440.

The previous prime is 33679. The next prime is 33703. The reversal of 33680 is 8633.

It can be written as a sum of positive squares in 2 ways, for example, as 4096 + 29584 = 64^2 + 172^2 .

It is a tau number, because it is divible by the number of its divisors (20).

It is a super-2 number, since 2×33680² = 2268684800, which contains 22 as substring.

It is a Smith number, since the sum of its digits (20) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (20).

It is a plaindrome in base 11.

It is an unprimeable number.

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, 131 + ... + 290.

2³³⁶⁸⁰ is an apocalyptic number.

It is an amenable number.

33680 is an abundant number, since it is smaller than the sum of its proper divisors (44812).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (39246).

33680 is a wasteful number, since it uses less digits than its factorization.

33680 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 434 (or 428 counting only the distinct ones).

The product of its (nonzero) digits is 432, while the sum is 20.

The square root of 33680 is about 183.5211159513. The cubic root of 33680 is about 32.2941626005.

The spelling of 33680 in words is "thirty-three thousand, six hundred eighty".