What are the numbers divisible by 2000?

2000, 4000, 6000, 8000, 10000, 12000, 14000, 16000, 18000, 20000, 22000, 24000, 26000, 28000, 30000, 32000, 34000, 36000, 38000, 40000, 42000, 44000, 46000, 48000, 50000, 52000, 54000, 56000, 58000, 60000, 62000, 64000, 66000, 68000, 70000, 72000, 74000, 76000, 78000, 80000, 82000, 84000, 86000, 88000, 90000, 92000, 94000, 96000, 98000, 100000

There is a total of 50 numbers (up to 100000) that are divisible by 2000.
The sum of these numbers is 2550000.
The arithmetic mean of these numbers is 51000.

How to find the numbers divisible by 2000?

Finding all the numbers that can be divided by 2000 is essentially the same as searching for the multiples of 2000: if a number N is a multiple of 2000, then 2000 is a divisor of N.

Indeed, if we assume that N is a multiple of 2000, this means there exists an integer k such that:

$k \times 2000 = N$

Conversely, the result of N divided by 2000 is this same integer k (without any remainder):

$k = \frac{N}{2000}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2000 (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 2000 less than 100000):

1 × 2000 = 2000
2 × 2000 = 4000
3 × 2000 = 6000
...
49 × 2000 = 98000
50 × 2000 = 100000