What are the numbers divisible by 2010?

2010, 4020, 6030, 8040, 10050, 12060, 14070, 16080, 18090, 20100, 22110, 24120, 26130, 28140, 30150, 32160, 34170, 36180, 38190, 40200, 42210, 44220, 46230, 48240, 50250, 52260, 54270, 56280, 58290, 60300, 62310, 64320, 66330, 68340, 70350, 72360, 74370, 76380, 78390, 80400, 82410, 84420, 86430, 88440, 90450, 92460, 94470, 96480, 98490

There is a total of 49 numbers (up to 100000) that are divisible by 2010.
The sum of these numbers is 2462250.
The arithmetic mean of these numbers is 50250.

How to find the numbers divisible by 2010?

Finding all the numbers that can be divided by 2010 is essentially the same as searching for the multiples of 2010: if a number N is a multiple of 2010, then 2010 is a divisor of N.

Indeed, if we assume that N is a multiple of 2010, this means there exists an integer k such that:

$k \times 2010 = N$

Conversely, the result of N divided by 2010 is this same integer k (without any remainder):

$k = \frac{N}{2010}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2010 (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 2010 less than 100000):

1 × 2010 = 2010
2 × 2010 = 4020
3 × 2010 = 6030
...
48 × 2010 = 96480
49 × 2010 = 98490