What are the numbers divisible by 2101?

2101, 4202, 6303, 8404, 10505, 12606, 14707, 16808, 18909, 21010, 23111, 25212, 27313, 29414, 31515, 33616, 35717, 37818, 39919, 42020, 44121, 46222, 48323, 50424, 52525, 54626, 56727, 58828, 60929, 63030, 65131, 67232, 69333, 71434, 73535, 75636, 77737, 79838, 81939, 84040, 86141, 88242, 90343, 92444, 94545, 96646, 98747

There is a total of 47 numbers (up to 100000) that are divisible by 2101.
The sum of these numbers is 2369928.
The arithmetic mean of these numbers is 50424.

How to find the numbers divisible by 2101?

Finding all the numbers that can be divided by 2101 is essentially the same as searching for the multiples of 2101: if a number N is a multiple of 2101, then 2101 is a divisor of N.

Indeed, if we assume that N is a multiple of 2101, this means there exists an integer k such that:

$k \times 2101 = N$

Conversely, the result of N divided by 2101 is this same integer k (without any remainder):

$k = \frac{N}{2101}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2101 (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 2101 less than 100000):

1 × 2101 = 2101
2 × 2101 = 4202
3 × 2101 = 6303
...
46 × 2101 = 96646
47 × 2101 = 98747