23328 has 42 divisors (see below), whose sum is σ = 68859. Its totient is φ = 7776.

The previous prime is 23327. The next prime is 23333. The reversal of 23328 is 82332.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in only one way, i.e., 11664 + 11664 = 108^2 + 108^2 .

It is an ABA number since it can be written as A⋅B^{A}, here for A=2, B=108.

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 an enlightened number because it begins with the concatenation of its prime factors (23).

It is a nialpdrome in base 6 and base 8.

It is a self number, because there is not a number *n* which added to its sum of digits gives 23328.

It is not an unprimeable number, because it can be changed into a prime (23321) by changing a digit.

It is a polite number, since it can be written in 6 ways as a sum of consecutive naturals, for example, 7775 + 7776 + 7777.

23328 is a Friedman number, since it can be written as 32*3^(8-2), using all its digits and the basic arithmetic operations.

2^{23328} 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 23328

23328 is an abundant number, since it is smaller than the sum of its proper divisors (45531).

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

23328 is an frugal number, since it uses more digits than its factorization.

23328 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 28 (or 5 counting only the distinct ones).

The product of its digits is 288, while the sum is 18.

The square root of 23328 is about 152.7350647363. The cubic root of 23328 is about 28.5732189354.

Multiplying 23328 by its sum of digits (18), we get a square (419904 = 648^{2}).

23328 divided by its sum of digits (18) gives a 4-th power (1296 = 6^{4}).

Multiplying 23328 by its product of digits (288), we get a square (6718464 = 2592^{2}).

23328 divided by its product of digits (288) gives a 4-th power (81 = 3^{4}).

It can be divided in two parts, 23 and 328, that added together give a triangular number (351 = T_{26}).

The spelling of 23328 in words is "twenty-three thousand, three hundred twenty-eight".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 72 81 96 108 144 162 216 243 288 324 432 486 648 729 864 972 1296 1458 1944 2592 2916 3888 5832 7776 11664 23328

• e-mail: info -at- numbersaplenty.com • Privacy notice • done in 0.110 sec. • engine limits •