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 is an ABA number since it can be written as A⋅BA, here for A=8, B=2.
It is a d-powerful number, because it can be written as 29 + 45 + 0 + 83 .
It is a Duffinian number.
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 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 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 = 217).
2048 divided by its product of nonzero digits (64) gives a 5-th power (32 = 25).
The spelling of 2048 in words is "two thousand, forty-eight".