What are the numbers divisible by 2106?

2106, 4212, 6318, 8424, 10530, 12636, 14742, 16848, 18954, 21060, 23166, 25272, 27378, 29484, 31590, 33696, 35802, 37908, 40014, 42120, 44226, 46332, 48438, 50544, 52650, 54756, 56862, 58968, 61074, 63180, 65286, 67392, 69498, 71604, 73710, 75816, 77922, 80028, 82134, 84240, 86346, 88452, 90558, 92664, 94770, 96876, 98982

There is a total of 47 numbers (up to 100000) that are divisible by 2106.
The sum of these numbers is 2375568.
The arithmetic mean of these numbers is 50544.

How to find the numbers divisible by 2106?

Finding all the numbers that can be divided by 2106 is essentially the same as searching for the multiples of 2106: if a number N is a multiple of 2106, then 2106 is a divisor of N.

Indeed, if we assume that N is a multiple of 2106, this means there exists an integer k such that:

$k \times 2106 = N$

Conversely, the result of N divided by 2106 is this same integer k (without any remainder):

$k = \frac{N}{2106}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2106 (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 2106 less than 100000):

1 × 2106 = 2106
2 × 2106 = 4212
3 × 2106 = 6318
...
46 × 2106 = 96876
47 × 2106 = 98982