33408 has 48 divisors (see below), whose sum is σ = 99450. Its totient is φ = 10752.

The previous prime is 33403. The next prime is 33409. The reversal of 33408 is 80433.

It can be written as a sum of positive squares in only one way, i.e., 28224 + 5184 = 168^2 + 72^2 .

It is a tau number, because it is divible by the number of its divisors (48).

It is a super-2 number, since 2×33408² = 2232188928, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a plaindrome in base 13.

It is not an unprimeable number, because it can be changed into a prime (33403) by changing a digit.

33408 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 5 ways as a sum of consecutive naturals, for example, 1138 + ... + 1166.

2³³⁴⁰⁸ 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 33408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (49725).

33408 is an abundant number, since it is smaller than the sum of its proper divisors (66042).

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

33408 is a wasteful number, since it uses less digits than its factorization.

33408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 49 (or 34 counting only the distinct ones).

The product of its (nonzero) digits is 288, while the sum is 18.

The square root of 33408 is about 182.7785545407. The cubic root of 33408 is about 32.2069915248.

It can be divided in two parts, 33 and 408, that added together give a square (441 = 21²).

The spelling of 33408 in words is "thirty-three thousand, four hundred eight".