What are the numbers divisible by 2006?

2006, 4012, 6018, 8024, 10030, 12036, 14042, 16048, 18054, 20060, 22066, 24072, 26078, 28084, 30090, 32096, 34102, 36108, 38114, 40120, 42126, 44132, 46138, 48144, 50150, 52156, 54162, 56168, 58174, 60180, 62186, 64192, 66198, 68204, 70210, 72216, 74222, 76228, 78234, 80240, 82246, 84252, 86258, 88264, 90270, 92276, 94282, 96288, 98294

There is a total of 49 numbers (up to 100000) that are divisible by 2006.
The sum of these numbers is 2457350.
The arithmetic mean of these numbers is 50150.

How to find the numbers divisible by 2006?

Finding all the numbers that can be divided by 2006 is essentially the same as searching for the multiples of 2006: if a number N is a multiple of 2006, then 2006 is a divisor of N.

Indeed, if we assume that N is a multiple of 2006, this means there exists an integer k such that:

$k \times 2006 = N$

Conversely, the result of N divided by 2006 is this same integer k (without any remainder):

$k = \frac{N}{2006}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2006 (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 2006 less than 100000):

1 × 2006 = 2006
2 × 2006 = 4012
3 × 2006 = 6018
...
48 × 2006 = 96288
49 × 2006 = 98294