13824 has 40 divisors (see below), whose sum is σ = 40920. Its totient is φ = 4608.

The previous prime is 13807. The next prime is 13829. The reversal of 13824 is 42831.

It is a happy number.

The cubic root of 13824 is 24.

It is a perfect power (a cube), and thus also a powerful number.

It is a Jordan-Polya number, since it can be written as (4!)^{3}.

It is a super-2 number, since 2×13824^{2} = 382205952, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

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 one of the 548 Lynch-Bell numbers.

It is a nialpdrome in base 8 and base 12.

It is a zygodrome in base 8.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 13797 and 13806.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (13829) by changing a digit.

13824 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 4607 + 4608 + 4609.

It is an arithmetic number, because the mean of its divisors is an integer number (1023).

13824 is a Friedman number, since it can be written as (18+4+2)^3, using all its digits and the basic arithmetic operations.

2^{13824} 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 13824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (20460).

13824 is an abundant number, since it is smaller than the sum of its proper divisors (27096).

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

13824 is an frugal number, since it uses more digits than its factorization.

13824 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 27 (or 5 counting only the distinct ones).

The product of its digits is 192, while the sum is 18.

The square root of 13824 is about 117.5755076536.

Multiplying 13824 by its sum of digits (18), we get a 5-th power (248832 = 12^{5}).

The spelling of 13824 in words is "thirteen thousand, eight hundred twenty-four".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 96 108 128 144 192 216 256 288 384 432 512 576 768 864 1152 1536 1728 2304 3456 4608 6912 13824

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