What are the numbers divisible by 4007?

4007, 8014, 12021, 16028, 20035, 24042, 28049, 32056, 36063, 40070, 44077, 48084, 52091, 56098, 60105, 64112, 68119, 72126, 76133, 80140, 84147, 88154, 92161, 96168

There is a total of 24 numbers (up to 100000) that are divisible by 4007.
The sum of these numbers is 1202100.
The arithmetic mean of these numbers is 50087.5.

How to find the numbers divisible by 4007?

Finding all the numbers that can be divided by 4007 is essentially the same as searching for the multiples of 4007: if a number N is a multiple of 4007, then 4007 is a divisor of N.

Indeed, if we assume that N is a multiple of 4007, this means there exists an integer k such that:

$k \times 4007 = N$

Conversely, the result of N divided by 4007 is this same integer k (without any remainder):

$k = \frac{N}{4007}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 4007 (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 4007 less than 100000):

1 × 4007 = 4007
2 × 4007 = 8014
3 × 4007 = 12021
...
23 × 4007 = 92161
24 × 4007 = 96168