What are the numbers divisible by 4100?

4100, 8200, 12300, 16400, 20500, 24600, 28700, 32800, 36900, 41000, 45100, 49200, 53300, 57400, 61500, 65600, 69700, 73800, 77900, 82000, 86100, 90200, 94300, 98400

There is a total of 24 numbers (up to 100000) that are divisible by 4100.
The sum of these numbers is 1230000.
The arithmetic mean of these numbers is 51250.

How to find the numbers divisible by 4100?

Finding all the numbers that can be divided by 4100 is essentially the same as searching for the multiples of 4100: if a number N is a multiple of 4100, then 4100 is a divisor of N.

Indeed, if we assume that N is a multiple of 4100, this means there exists an integer k such that:

$k \times 4100 = N$

Conversely, the result of N divided by 4100 is this same integer k (without any remainder):

$k = \frac{N}{4100}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 4100 (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 4100 less than 100000):

1 × 4100 = 4100
2 × 4100 = 8200
3 × 4100 = 12300
...
23 × 4100 = 94300
24 × 4100 = 98400