213200 has 60 divisors (see below), whose sum is σ = 565068. Its totient is φ = 76800.

The previous prime is 213193. The next prime is 213203. The reversal of 213200 is 2312.

213200 = 11³ + 12³ + ... + 30³.

It can be written as a sum of positive squares in 6 ways, for example, as 71824 + 141376 = 268^2 + 376^2 .

It is a Harshad number since it is a multiple of its sum of digits (8).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (213203) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 5180 + ... + 5220.

2²¹³²⁰⁰ is an apocalyptic number.

213200 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 213200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (282534).

213200 is an abundant number, since it is smaller than the sum of its proper divisors (351868).

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

213200 is a wasteful number, since it uses less digits than its factorization.

213200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 72 (or 61 counting only the distinct ones).

The product of its (nonzero) digits is 12, while the sum is 8.

The square root of 213200 is about 461.7358552246. The cubic root of 213200 is about 59.7396123466.

Adding to 213200 its reverse (2312), we get a palindrome (215512).

The spelling of 213200 in words is "two hundred thirteen thousand, two hundred".