2048 has 12 divisors (see below), whose sum is σ = 4095. Its totient is φ = 1024.

The previous prime is 2039. The next prime is 2053. The reversal of 2048 is 8402.

It is a perfect power (a 11-th power), and thus also a powerful number.

It is a Jordan-Polya number, since it can be written as (2!)^{11}.

2048 is an esthetic number in base 7, because in such base its adjacent digits differ by 1.

It can be written as a sum of positive squares in only one way, i.e., 1024 + 1024 = 32^2 + 32^2 .

It is an ABA number since it can be written as A⋅B^{A}, here for A=8, B=2.

It is a d-powerful number, because it can be written as **2**^{9} + **4**^{5} + **0** + **8**^{3} .

It is a cake number, because a cake can be divided into 2048 parts by 23 planar cuts.

It is a Duffinian number.

It is an enlightened number because it begins with the concatenation of its prime factors (2).

It is a plaindrome in base 12.

It is a nialpdrome in base 2, base 4, base 8, base 14 and base 16.

It is an unprimeable number.

2048 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

In principle, a polygon with 2048 sides can be constructed with ruler and compass.

It is an impolite number, since it cannot be written as a nontrivial sum of consecutive naturals.

2048 is a Friedman number, since it can be written as (8^4+0)/2, using all its digits and the basic arithmetic operations.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 2048

2048 is a deficient number, since it is larger than the sum of its proper divisors (2047).

2048 is an frugal number, since it uses more digits than its factorization.

2048 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 22 (or 2 counting only the distinct ones).

The product of its (nonzero) digits is 64, while the sum is 14.

The square root of 2048 is about 45.2548339959. The cubic root of 2048 is about 12.6992084157.

Adding to 2048 its product of nonzero digits (64), we get a palindrome (2112).

Multiplying 2048 by its product of nonzero digits (64), we get a 17-th power (131072 = 2^{17}).

2048 divided by its product of nonzero digits (64) gives a 5-th power (32 = 2^{5}).

It can be divided in two parts, 204 and 8, that added together give a palindrome (212).

The spelling of 2048 in words is "two thousand, forty-eight".

• e-mail: info -at- numbersaplenty.com • Privacy notice • done in 0.111 sec. • engine limits •