What are the numbers divisible by 2004?

2004, 4008, 6012, 8016, 10020, 12024, 14028, 16032, 18036, 20040, 22044, 24048, 26052, 28056, 30060, 32064, 34068, 36072, 38076, 40080, 42084, 44088, 46092, 48096, 50100, 52104, 54108, 56112, 58116, 60120, 62124, 64128, 66132, 68136, 70140, 72144, 74148, 76152, 78156, 80160, 82164, 84168, 86172, 88176, 90180, 92184, 94188, 96192, 98196

There is a total of 49 numbers (up to 100000) that are divisible by 2004.
The sum of these numbers is 2454900.
The arithmetic mean of these numbers is 50100.

How to find the numbers divisible by 2004?

Finding all the numbers that can be divided by 2004 is essentially the same as searching for the multiples of 2004: if a number N is a multiple of 2004, then 2004 is a divisor of N.

Indeed, if we assume that N is a multiple of 2004, this means there exists an integer k such that:

$k \times 2004 = N$

Conversely, the result of N divided by 2004 is this same integer k (without any remainder):

$k = \frac{N}{2004}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2004 (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 2004 less than 100000):

1 × 2004 = 2004
2 × 2004 = 4008
3 × 2004 = 6012
...
48 × 2004 = 96192
49 × 2004 = 98196