21312 has 42 divisors (see below), whose sum is σ = 62738. Its totient is φ = 6912.

The previous prime is 21283. The next prime is 21313.

It can be divided in two parts, 213 and 12, that multiplied together give a triangular number (2556 = T_{71}).

It is a happy number.

21312 is nontrivially palindromic in base 10.

It can be written as a sum of positive squares in only one way, i.e., 20736 + 576 = 144^2 + 24^2 .

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is a nialpdrome in base 9.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 21294 and 21303.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (21313) by changing a digit.

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 5 ways as a sum of consecutive naturals, for example, 558 + ... + 594.

2^{21312} 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 21312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (31369).

21312 is an abundant number, since it is smaller than the sum of its proper divisors (41426).

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

21312 is a wasteful number, since it uses less digits than its factorization.

21312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 55 (or 42 counting only the distinct ones).

The product of its digits is 12, while the sum is 9.

The square root of 21312 is about 145.9863007272. The cubic root of 21312 is about 27.7252030737.

The spelling of 21312 in words is "twenty-one thousand, three hundred twelve", and thus it is an iban number.

Divisors: 1 2 3 4 6 8 9 12 16 18 24 32 36 37 48 64 72 74 96 111 144 148 192 222 288 296 333 444 576 592 666 888 1184 1332 1776 2368 2664 3552 5328 7104 10656 21312

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