What are the numbers divisible by 2114?

2114, 4228, 6342, 8456, 10570, 12684, 14798, 16912, 19026, 21140, 23254, 25368, 27482, 29596, 31710, 33824, 35938, 38052, 40166, 42280, 44394, 46508, 48622, 50736, 52850, 54964, 57078, 59192, 61306, 63420, 65534, 67648, 69762, 71876, 73990, 76104, 78218, 80332, 82446, 84560, 86674, 88788, 90902, 93016, 95130, 97244, 99358

There is a total of 47 numbers (up to 100000) that are divisible by 2114.
The sum of these numbers is 2384592.
The arithmetic mean of these numbers is 50736.

How to find the numbers divisible by 2114?

Finding all the numbers that can be divided by 2114 is essentially the same as searching for the multiples of 2114: if a number N is a multiple of 2114, then 2114 is a divisor of N.

Indeed, if we assume that N is a multiple of 2114, this means there exists an integer k such that:

$k \times 2114 = N$

Conversely, the result of N divided by 2114 is this same integer k (without any remainder):

$k = \frac{N}{2114}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2114 (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 2114 less than 100000):

1 × 2114 = 2114
2 × 2114 = 4228
3 × 2114 = 6342
...
46 × 2114 = 97244
47 × 2114 = 99358