What are the numbers divisible by 2013?

2013, 4026, 6039, 8052, 10065, 12078, 14091, 16104, 18117, 20130, 22143, 24156, 26169, 28182, 30195, 32208, 34221, 36234, 38247, 40260, 42273, 44286, 46299, 48312, 50325, 52338, 54351, 56364, 58377, 60390, 62403, 64416, 66429, 68442, 70455, 72468, 74481, 76494, 78507, 80520, 82533, 84546, 86559, 88572, 90585, 92598, 94611, 96624, 98637

There is a total of 49 numbers (up to 100000) that are divisible by 2013.
The sum of these numbers is 2465925.
The arithmetic mean of these numbers is 50325.

How to find the numbers divisible by 2013?

Finding all the numbers that can be divided by 2013 is essentially the same as searching for the multiples of 2013: if a number N is a multiple of 2013, then 2013 is a divisor of N.

Indeed, if we assume that N is a multiple of 2013, this means there exists an integer k such that:

$k \times 2013 = N$

Conversely, the result of N divided by 2013 is this same integer k (without any remainder):

$k = \frac{N}{2013}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2013 (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 2013 less than 100000):

1 × 2013 = 2013
2 × 2013 = 4026
3 × 2013 = 6039
...
48 × 2013 = 96624
49 × 2013 = 98637