What are the numbers divisible by 2048?

2048, 4096, 6144, 8192, 10240, 12288, 14336, 16384, 18432, 20480, 22528, 24576, 26624, 28672, 30720, 32768, 34816, 36864, 38912, 40960, 43008, 45056, 47104, 49152, 51200, 53248, 55296, 57344, 59392, 61440, 63488, 65536, 67584, 69632, 71680, 73728, 75776, 77824, 79872, 81920, 83968, 86016, 88064, 90112, 92160, 94208, 96256, 98304

There is a total of 48 numbers (up to 100000) that are divisible by 2048.
The sum of these numbers is 2408448.
The arithmetic mean of these numbers is 50176.

How to find the numbers divisible by 2048?

Finding all the numbers that can be divided by 2048 is essentially the same as searching for the multiples of 2048: if a number N is a multiple of 2048, then 2048 is a divisor of N.

Indeed, if we assume that N is a multiple of 2048, this means there exists an integer k such that:

$k \times 2048 = N$

Conversely, the result of N divided by 2048 is this same integer k (without any remainder):

$k = \frac{N}{2048}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2048 (we can keep multiplying it by increasingly larger integers, without ever reaching the end).

However, in this instance, we've chosen to set an arbitrary limit (specifically, the multiples of 2048 less than 100000):

1 × 2048 = 2048
2 × 2048 = 4096
3 × 2048 = 6144
...
47 × 2048 = 96256
48 × 2048 = 98304