What are the numbers divisible by 8001?

8001, 16002, 24003, 32004, 40005, 48006, 56007, 64008, 72009, 80010, 88011, 96012

There is a total of 12 numbers (up to 100000) that are divisible by 8001.
The sum of these numbers is 624078.
The arithmetic mean of these numbers is 52006.5.

How to find the numbers divisible by 8001?

Finding all the numbers that can be divided by 8001 is essentially the same as searching for the multiples of 8001: if a number N is a multiple of 8001, then 8001 is a divisor of N.

Indeed, if we assume that N is a multiple of 8001, this means there exists an integer k such that:

$k \times 8001 = N$

Conversely, the result of N divided by 8001 is this same integer k (without any remainder):

$k = \frac{N}{8001}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 8001 (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 8001 less than 100000):

1 × 8001 = 8001
2 × 8001 = 16002
3 × 8001 = 24003
...
11 × 8001 = 88011
12 × 8001 = 96012