213312 has 56 divisors (see below), whose sum is σ = 621792. Its totient is φ = 64000.

The previous prime is 213307. The next prime is 213319.

It is a happy number.

213312 is nontrivially palindromic in base 10.

It is a Harshad number since it is a multiple of its sum of digits (12).

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (213319) by changing a digit.

213312 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 (5) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 2062 + ... + 2162.

2²¹³³¹² is an apocalyptic number.

213312 is a gapful number since it is divisible by the number (22) 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 213312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (310896).

213312 is an abundant number, since it is smaller than the sum of its proper divisors (408480).

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

213312 is a wasteful number, since it uses less digits than its factorization.

213312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 127 (or 117 counting only the distinct ones).

The product of its digits is 36, while the sum is 12.

The square root of 213312 is about 461.8571207636. The cubic root of 213312 is about 59.7500714856.

It can be divided in two parts, 2133 and 12, that added together give a triangular number (2145 = T₆₅).

The spelling of 213312 in words is "two hundred thirteen thousand, three hundred twelve".