218400 has 144 divisors (see below), whose sum is σ = 874944. Its totient is φ = 46080.

The previous prime is 218389. The next prime is 218401. The reversal of 218400 is 4812.

218400 = 25² + 26² + ... + 87².

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a self number, because there is not a number n which added to its sum of digits gives 218400.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (218401) by changing a digit.

218400 is an untouchable number, because it is not equal to the sum of proper divisors of any 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 23 ways as a sum of consecutive naturals, for example, 16794 + ... + 16806.

It is an arithmetic number, because the mean of its divisors is an integer number (6076).

2²¹⁸⁴⁰⁰ is an apocalyptic number.

218400 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 218400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (437472).

218400 is an abundant number, since it is smaller than the sum of its proper divisors (656544).

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

218400 is a wasteful number, since it uses less digits than its factorization.

218400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 43 (or 30 counting only the distinct ones).

The product of its (nonzero) digits is 64, while the sum is 15.

The square root of 218400 is about 467.3328578219. The cubic root of 218400 is about 60.2214042202.

It can be divided in two parts, 21 and 8400, that multiplied together give a square (176400 = 420²).

The spelling of 218400 in words is "two hundred eighteen thousand, four hundred".