217664000 has 160 divisors (see below), whose sum is σ = 574516800. Its totient is φ = 82022400.

The previous prime is 217663997. The next prime is 217664009. The reversal of 217664000 is 466712.

It is a tau number, because it is divible by the number of its divisors (160).

It is not an unprimeable number, because it can be changed into a prime (217664009) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1215911 + ... + 1216089.

It is an arithmetic number, because the mean of its divisors is an integer number (3590730).

Almost surely, 2^217664000 is an apocalyptic number.

217664000 is a gapful number since it is divisible by the number (20) 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 217664000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (287258400).

217664000 is an abundant number, since it is smaller than the sum of its proper divisors (356852800).

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

217664000 is an equidigital number, since it uses as much as digits as its factorization.

217664000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 231 (or 205 counting only the distinct ones).

The product of its (nonzero) digits is 2016, while the sum is 26.

The square root of 217664000 is about 14753.4402767626. The cubic root of 217664000 is about 601.5368011173.

The spelling of 217664000 in words is "two hundred seventeen million, six hundred sixty-four thousand".