What are the numbers divisible by 2113?

2113, 4226, 6339, 8452, 10565, 12678, 14791, 16904, 19017, 21130, 23243, 25356, 27469, 29582, 31695, 33808, 35921, 38034, 40147, 42260, 44373, 46486, 48599, 50712, 52825, 54938, 57051, 59164, 61277, 63390, 65503, 67616, 69729, 71842, 73955, 76068, 78181, 80294, 82407, 84520, 86633, 88746, 90859, 92972, 95085, 97198, 99311

There is a total of 47 numbers (up to 100000) that are divisible by 2113.
The sum of these numbers is 2383464.
The arithmetic mean of these numbers is 50712.

How to find the numbers divisible by 2113?

Finding all the numbers that can be divided by 2113 is essentially the same as searching for the multiples of 2113: if a number N is a multiple of 2113, then 2113 is a divisor of N.

Indeed, if we assume that N is a multiple of 2113, this means there exists an integer k such that:

$k \times 2113 = N$

Conversely, the result of N divided by 2113 is this same integer k (without any remainder):

$k = \frac{N}{2113}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2113 (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 2113 less than 100000):

1 × 2113 = 2113
2 × 2113 = 4226
3 × 2113 = 6339
...
46 × 2113 = 97198
47 × 2113 = 99311