213418800 has 300 divisors, whose sum is σ = 876293616. Its totient is φ = 48729600.

The previous prime is 213418783. The next prime is 213418831. The reversal of 213418800 is 8814312.

213418800 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (300).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nialpdrome in base 16.

It is an unprimeable number.

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 59 ways as a sum of consecutive naturals, for example, 226330 + ... + 227270.

Almost surely, 2^213418800 is an apocalyptic number.

213418800 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 213418800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (438146808).

213418800 is an abundant number, since it is smaller than the sum of its proper divisors (662874816).

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

213418800 is a wasteful number, since it uses less digits than its factorization.

213418800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 978 (or 958 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 27.

The square root of 213418800 is about 14608.8603251588. The cubic root of 213418800 is about 597.6004161220.

The spelling of 213418800 in words is "two hundred thirteen million, four hundred eighteen thousand, eight hundred".