What are the numbers divisible by 2009?

2009, 4018, 6027, 8036, 10045, 12054, 14063, 16072, 18081, 20090, 22099, 24108, 26117, 28126, 30135, 32144, 34153, 36162, 38171, 40180, 42189, 44198, 46207, 48216, 50225, 52234, 54243, 56252, 58261, 60270, 62279, 64288, 66297, 68306, 70315, 72324, 74333, 76342, 78351, 80360, 82369, 84378, 86387, 88396, 90405, 92414, 94423, 96432, 98441

There is a total of 49 numbers (up to 100000) that are divisible by 2009.
The sum of these numbers is 2461025.
The arithmetic mean of these numbers is 50225.

How to find the numbers divisible by 2009?

Finding all the numbers that can be divided by 2009 is essentially the same as searching for the multiples of 2009: if a number N is a multiple of 2009, then 2009 is a divisor of N.

Indeed, if we assume that N is a multiple of 2009, this means there exists an integer k such that:

$k \times 2009 = N$

Conversely, the result of N divided by 2009 is this same integer k (without any remainder):

$k = \frac{N}{2009}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2009 (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 2009 less than 100000):

1 × 2009 = 2009
2 × 2009 = 4018
3 × 2009 = 6027
...
48 × 2009 = 96432
49 × 2009 = 98441