What are the numbers divisible by 3007?

3007, 6014, 9021, 12028, 15035, 18042, 21049, 24056, 27063, 30070, 33077, 36084, 39091, 42098, 45105, 48112, 51119, 54126, 57133, 60140, 63147, 66154, 69161, 72168, 75175, 78182, 81189, 84196, 87203, 90210, 93217, 96224, 99231

There is a total of 33 numbers (up to 100000) that are divisible by 3007.
The sum of these numbers is 1686927.
The arithmetic mean of these numbers is 51119.

How to find the numbers divisible by 3007?

Finding all the numbers that can be divided by 3007 is essentially the same as searching for the multiples of 3007: if a number N is a multiple of 3007, then 3007 is a divisor of N.

Indeed, if we assume that N is a multiple of 3007, this means there exists an integer k such that:

$k \times 3007 = N$

Conversely, the result of N divided by 3007 is this same integer k (without any remainder):

$k = \frac{N}{3007}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 3007 (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 3007 less than 100000):

1 × 3007 = 3007
2 × 3007 = 6014
3 × 3007 = 9021
...
32 × 3007 = 96224
33 × 3007 = 99231