33872000 has 128 divisors (see below), whose sum is σ = 88311600. Its totient is φ = 12902400.

The previous prime is 33871993. The next prime is 33872011. The reversal of 33872000 is 27833.

It can be written as a sum of positive squares in 8 ways, for example, as 1700416 + 32171584 = 1304^2 + 5672^2 .

It is a tau number, because it is divible by the number of its divisors (128).

It is a super-2 number, since 2×33872000² = 2294624768000000, which contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

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 15 ways as a sum of consecutive naturals, for example, 463964 + ... + 464036.

Almost surely, 2^33872000 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 33872000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (44155800).

33872000 is an abundant number, since it is smaller than the sum of its proper divisors (54439600).

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

33872000 is an equidigital number, since it uses as much as digits as its factorization.

33872000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 131 (or 109 counting only the distinct ones).

The product of its (nonzero) digits is 1008, while the sum is 23.

The square root of 33872000 is about 5819.9656356374. The cubic root of 33872000 is about 323.5541293706.

Adding to 33872000 its reverse (27833), we get a palindrome (33899833).

The spelling of 33872000 in words is "thirty-three million, eight hundred seventy-two thousand".