What are the numbers divisible by 3003?

3003, 6006, 9009, 12012, 15015, 18018, 21021, 24024, 27027, 30030, 33033, 36036, 39039, 42042, 45045, 48048, 51051, 54054, 57057, 60060, 63063, 66066, 69069, 72072, 75075, 78078, 81081, 84084, 87087, 90090, 93093, 96096, 99099

There is a total of 33 numbers (up to 100000) that are divisible by 3003.
The sum of these numbers is 1684683.
The arithmetic mean of these numbers is 51051.

How to find the numbers divisible by 3003?

Finding all the numbers that can be divided by 3003 is essentially the same as searching for the multiples of 3003: if a number N is a multiple of 3003, then 3003 is a divisor of N.

Indeed, if we assume that N is a multiple of 3003, this means there exists an integer k such that:

$k \times 3003 = N$

Conversely, the result of N divided by 3003 is this same integer k (without any remainder):

$k = \frac{N}{3003}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 3003 (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 3003 less than 100000):

1 × 3003 = 3003
2 × 3003 = 6006
3 × 3003 = 9009
...
32 × 3003 = 96096
33 × 3003 = 99099