133584000 has 384 divisors, whose sum is σ = 507911040. Its totient is φ = 30976000.

The previous prime is 133583993. The next prime is 133584001. The reversal of 133584000 is 485331.

It is a tau number, because it is divible by the number of its divisors (384).

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

It is not an unprimeable number, because it can be changed into a prime (133584001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 5807989 + ... + 5808011.

It is an arithmetic number, because the mean of its divisors is an integer number (1322685).

Almost surely, 2^133584000 is an apocalyptic number.

133584000 is a gapful number since it is divisible by the number (10) 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 133584000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (253955520).

133584000 is an abundant number, since it is smaller than the sum of its proper divisors (374327040).

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

133584000 is a wasteful number, since it uses less digits than its factorization.

133584000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 77 (or 44 counting only the distinct ones).

The product of its (nonzero) digits is 1440, while the sum is 24.

The square root of 133584000 is about 11557.8544721761. The cubic root of 133584000 is about 511.1929015646.

The spelling of 133584000 in words is "one hundred thirty-three million, five hundred eighty-four thousand".