214800 has 60 divisors (see below), whose sum is σ = 691920. Its totient is φ = 56960.

The previous prime is 214789. The next prime is 214807. The reversal of 214800 is 8412.

It is a tau number, because it is divible by the number of its divisors (60).

It is a super-2 number, since 2×214800² = 92278080000, which contains 22 as substring.

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 214800.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 214800.

It is not an unprimeable number, because it can be changed into a prime (214807) by changing a digit.

214800 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 11 ways as a sum of consecutive naturals, for example, 1111 + ... + 1289.

It is an arithmetic number, because the mean of its divisors is an integer number (11532).

2²¹⁴⁸⁰⁰ is an apocalyptic number.

214800 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 214800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (345960).

214800 is an abundant number, since it is smaller than the sum of its proper divisors (477120).

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

214800 is a wasteful number, since it uses less digits than its factorization.

214800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 200 (or 189 counting only the distinct ones).

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

The square root of 214800 is about 463.4652090503. The cubic root of 214800 is about 59.8886824901. Note that the first 3 decimals are identical.

The spelling of 214800 in words is "two hundred fourteen thousand, eight hundred".