What are the numbers divisible by 4095?

4095, 8190, 12285, 16380, 20475, 24570, 28665, 32760, 36855, 40950, 45045, 49140, 53235, 57330, 61425, 65520, 69615, 73710, 77805, 81900, 85995, 90090, 94185, 98280

There is a total of 24 numbers (up to 100000) that are divisible by 4095.
The sum of these numbers is 1228500.
The arithmetic mean of these numbers is 51187.5.

How to find the numbers divisible by 4095?

Finding all the numbers that can be divided by 4095 is essentially the same as searching for the multiples of 4095: if a number N is a multiple of 4095, then 4095 is a divisor of N.

Indeed, if we assume that N is a multiple of 4095, this means there exists an integer k such that:

$k \times 4095 = N$

Conversely, the result of N divided by 4095 is this same integer k (without any remainder):

$k = \frac{N}{4095}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 4095 (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 4095 less than 100000):

1 × 4095 = 4095
2 × 4095 = 8190
3 × 4095 = 12285
...
23 × 4095 = 94185
24 × 4095 = 98280