What are the numbers divisible by 2019?

2019, 4038, 6057, 8076, 10095, 12114, 14133, 16152, 18171, 20190, 22209, 24228, 26247, 28266, 30285, 32304, 34323, 36342, 38361, 40380, 42399, 44418, 46437, 48456, 50475, 52494, 54513, 56532, 58551, 60570, 62589, 64608, 66627, 68646, 70665, 72684, 74703, 76722, 78741, 80760, 82779, 84798, 86817, 88836, 90855, 92874, 94893, 96912, 98931

There is a total of 49 numbers (up to 100000) that are divisible by 2019.
The sum of these numbers is 2473275.
The arithmetic mean of these numbers is 50475.

How to find the numbers divisible by 2019?

Finding all the numbers that can be divided by 2019 is essentially the same as searching for the multiples of 2019: if a number N is a multiple of 2019, then 2019 is a divisor of N.

Indeed, if we assume that N is a multiple of 2019, this means there exists an integer k such that:

$k \times 2019 = N$

Conversely, the result of N divided by 2019 is this same integer k (without any remainder):

$k = \frac{N}{2019}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2019 (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 2019 less than 100000):

1 × 2019 = 2019
2 × 2019 = 4038
3 × 2019 = 6057
...
48 × 2019 = 96912
49 × 2019 = 98931