What are the numbers divisible by 2007?

2007, 4014, 6021, 8028, 10035, 12042, 14049, 16056, 18063, 20070, 22077, 24084, 26091, 28098, 30105, 32112, 34119, 36126, 38133, 40140, 42147, 44154, 46161, 48168, 50175, 52182, 54189, 56196, 58203, 60210, 62217, 64224, 66231, 68238, 70245, 72252, 74259, 76266, 78273, 80280, 82287, 84294, 86301, 88308, 90315, 92322, 94329, 96336, 98343

There is a total of 49 numbers (up to 100000) that are divisible by 2007.
The sum of these numbers is 2458575.
The arithmetic mean of these numbers is 50175.

How to find the numbers divisible by 2007?

Finding all the numbers that can be divided by 2007 is essentially the same as searching for the multiples of 2007: if a number N is a multiple of 2007, then 2007 is a divisor of N.

Indeed, if we assume that N is a multiple of 2007, this means there exists an integer k such that:

$k \times 2007 = N$

Conversely, the result of N divided by 2007 is this same integer k (without any remainder):

$k = \frac{N}{2007}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2007 (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 2007 less than 100000):

1 × 2007 = 2007
2 × 2007 = 4014
3 × 2007 = 6021
...
48 × 2007 = 96336
49 × 2007 = 98343