What are the numbers divisible by 2100?

2100, 4200, 6300, 8400, 10500, 12600, 14700, 16800, 18900, 21000, 23100, 25200, 27300, 29400, 31500, 33600, 35700, 37800, 39900, 42000, 44100, 46200, 48300, 50400, 52500, 54600, 56700, 58800, 60900, 63000, 65100, 67200, 69300, 71400, 73500, 75600, 77700, 79800, 81900, 84000, 86100, 88200, 90300, 92400, 94500, 96600, 98700

There is a total of 47 numbers (up to 100000) that are divisible by 2100.
The sum of these numbers is 2368800.
The arithmetic mean of these numbers is 50400.

How to find the numbers divisible by 2100?

Finding all the numbers that can be divided by 2100 is essentially the same as searching for the multiples of 2100: if a number N is a multiple of 2100, then 2100 is a divisor of N.

Indeed, if we assume that N is a multiple of 2100, this means there exists an integer k such that:

$k \times 2100 = N$

Conversely, the result of N divided by 2100 is this same integer k (without any remainder):

$k = \frac{N}{2100}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2100 (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 2100 less than 100000):

1 × 2100 = 2100
2 × 2100 = 4200
3 × 2100 = 6300
...
46 × 2100 = 96600
47 × 2100 = 98700