What are the numbers divisible by 3000?

3000, 6000, 9000, 12000, 15000, 18000, 21000, 24000, 27000, 30000, 33000, 36000, 39000, 42000, 45000, 48000, 51000, 54000, 57000, 60000, 63000, 66000, 69000, 72000, 75000, 78000, 81000, 84000, 87000, 90000, 93000, 96000, 99000

There is a total of 33 numbers (up to 100000) that are divisible by 3000.
The sum of these numbers is 1683000.
The arithmetic mean of these numbers is 51000.

How to find the numbers divisible by 3000?

Finding all the numbers that can be divided by 3000 is essentially the same as searching for the multiples of 3000: if a number N is a multiple of 3000, then 3000 is a divisor of N.

Indeed, if we assume that N is a multiple of 3000, this means there exists an integer k such that:

$k \times 3000 = N$

Conversely, the result of N divided by 3000 is this same integer k (without any remainder):

$k = \frac{N}{3000}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 3000 (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 3000 less than 100000):

1 × 3000 = 3000
2 × 3000 = 6000
3 × 3000 = 9000
...
32 × 3000 = 96000
33 × 3000 = 99000