What are the numbers divisible by 2109?

2109, 4218, 6327, 8436, 10545, 12654, 14763, 16872, 18981, 21090, 23199, 25308, 27417, 29526, 31635, 33744, 35853, 37962, 40071, 42180, 44289, 46398, 48507, 50616, 52725, 54834, 56943, 59052, 61161, 63270, 65379, 67488, 69597, 71706, 73815, 75924, 78033, 80142, 82251, 84360, 86469, 88578, 90687, 92796, 94905, 97014, 99123

There is a total of 47 numbers (up to 100000) that are divisible by 2109.
The sum of these numbers is 2378952.
The arithmetic mean of these numbers is 50616.

How to find the numbers divisible by 2109?

Finding all the numbers that can be divided by 2109 is essentially the same as searching for the multiples of 2109: if a number N is a multiple of 2109, then 2109 is a divisor of N.

Indeed, if we assume that N is a multiple of 2109, this means there exists an integer k such that:

$k \times 2109 = N$

Conversely, the result of N divided by 2109 is this same integer k (without any remainder):

$k = \frac{N}{2109}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2109 (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 2109 less than 100000):

1 × 2109 = 2109
2 × 2109 = 4218
3 × 2109 = 6327
...
46 × 2109 = 97014
47 × 2109 = 99123