213824 has 28 divisors (see below), whose sum is σ = 458724. Its totient is φ = 98304.

The previous prime is 213821. The next prime is 213827. The reversal of 213824 is 428312.

It is an interprime number because it is at equal distance from previous prime (213821) and next prime (213827).

It can be written as a sum of positive squares in 2 ways, for example, as 135424 + 78400 = 368^2 + 280^2 .

It is a hoax number, since the sum of its digits (20) coincides with the sum of the digits of its distinct prime factors.

It is a nialpdrome in base 13.

It is a junction number, because it is equal to n+sod(n) for n = 213796 and 213805.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 213824.

It is not an unprimeable number, because it can be changed into a prime (213821) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 704 + ... + 960.

It is an arithmetic number, because the mean of its divisors is an integer number (16383).

2²¹³⁸²⁴ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 213824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (229362).

213824 is an abundant number, since it is smaller than the sum of its proper divisors (244900).

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

213824 is a wasteful number, since it uses less digits than its factorization.

213824 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 282 (or 272 counting only the distinct ones).

The product of its digits is 384, while the sum is 20.

The square root of 213824 is about 462.4110725318. The cubic root of 213824 is about 59.7978381265.

The spelling of 213824 in words is "two hundred thirteen thousand, eight hundred twenty-four".