33800 has 36 divisors (see below), whose sum is σ = 85095. Its totient is φ = 12480.

The previous prime is 33797. The next prime is 33809. The reversal of 33800 is 833.

33800 = T₃₉ + T₄₀ + ... + T₆₃.

It is a happy number.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in 5 ways, for example, as 2116 + 31684 = 46^2 + 178^2 .

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=130.

It is a super-2 number, since 2×33800² = 2284880000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (33809) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 2594 + ... + 2606.

2³³⁸⁰⁰ 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 33800

33800 is an abundant number, since it is smaller than the sum of its proper divisors (51295).

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

33800 is a wasteful number, since it uses less digits than its factorization.

33800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 42 (or 20 counting only the distinct ones).

The product of its (nonzero) digits is 72, while the sum is 14.

The square root of 33800 is about 183.8477631085. The cubic root of 33800 is about 32.3324712516.

Multiplying 33800 by its product of nonzero digits (72), we get a square (2433600 = 1560²).

The spelling of 33800 in words is "thirty-three thousand, eight hundred".