What are the numbers divisible by 3009?

3009, 6018, 9027, 12036, 15045, 18054, 21063, 24072, 27081, 30090, 33099, 36108, 39117, 42126, 45135, 48144, 51153, 54162, 57171, 60180, 63189, 66198, 69207, 72216, 75225, 78234, 81243, 84252, 87261, 90270, 93279, 96288, 99297

There is a total of 33 numbers (up to 100000) that are divisible by 3009.
The sum of these numbers is 1688049.
The arithmetic mean of these numbers is 51153.

How to find the numbers divisible by 3009?

Finding all the numbers that can be divided by 3009 is essentially the same as searching for the multiples of 3009: if a number N is a multiple of 3009, then 3009 is a divisor of N.

Indeed, if we assume that N is a multiple of 3009, this means there exists an integer k such that:

$k \times 3009 = N$

Conversely, the result of N divided by 3009 is this same integer k (without any remainder):

$k = \frac{N}{3009}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 3009 (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 3009 less than 100000):

1 × 3009 = 3009
2 × 3009 = 6018
3 × 3009 = 9027
...
32 × 3009 = 96288
33 × 3009 = 99297