33628800 has 192 divisors, whose sum is σ = 115349760. Its totient is φ = 8601600.

The previous prime is 33628787. The next prime is 33628801. The reversal of 33628800 is 882633.

It is a tau number, because it is divible by the number of its divisors (192).

It is a super-2 number, since 2×33628800² = 2261792378880000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is not an unprimeable number, because it can be changed into a prime (33628801) 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 23 ways as a sum of consecutive naturals, for example, 297544 + ... + 297656.

It is an arithmetic number, because the mean of its divisors is an integer number (600780).

Almost surely, 2^33628800 is an apocalyptic number.

33628800 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 33628800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (57674880).

33628800 is an abundant number, since it is smaller than the sum of its proper divisors (81720960).

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

33628800 is a wasteful number, since it uses less digits than its factorization.

33628800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 171 (or 154 counting only the distinct ones).

The product of its (nonzero) digits is 6912, while the sum is 30.

The square root of 33628800 is about 5799.0344023811. The cubic root of 33628800 is about 322.7778987984. Note that the first 3 decimals are identical.

The spelling of 33628800 in words is "thirty-three million, six hundred twenty-eight thousand, eight hundred".