33864000 has 224 divisors, whose sum is σ = 119822976. Its totient is φ = 8396800.

The previous prime is 33863989. The next prime is 33864001. The reversal of 33864000 is 46833.

It is a super-2 number, since 2×33864000² = 2293540992000000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (33864001) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 407959 + ... + 408041.

It is an arithmetic number, because the mean of its divisors is an integer number (534924).

Almost surely, 2^33864000 is an apocalyptic number.

33864000 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 33864000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (59911488).

33864000 is an abundant number, since it is smaller than the sum of its proper divisors (85958976).

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

33864000 is a wasteful number, since it uses less digits than its factorization.

33864000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 130 (or 110 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 24.

The square root of 33864000 is about 5819.2783057695. The cubic root of 33864000 is about 323.5286546733.

The spelling of 33864000 in words is "thirty-three million, eight hundred sixty-four thousand".