What are the numbers divisible by 500?

500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 5500, 6000, 6500, 7000, 7500, 8000, 8500, 9000, 9500, 10000, 10500, 11000, 11500, 12000, 12500, 13000, 13500, 14000, 14500, 15000, 15500, 16000, 16500, 17000, 17500, 18000, 18500, 19000, 19500, 20000, 20500, 21000, 21500, 22000, 22500, 23000, 23500, 24000, 24500, 25000, 25500, 26000, 26500, 27000, 27500, 28000, 28500, 29000, 29500, 30000, 30500, 31000, 31500, 32000, 32500, 33000, 33500, 34000, 34500, 35000, 35500, 36000, 36500, 37000, 37500, 38000, 38500, 39000, 39500, 40000, 40500, 41000, 41500, 42000, 42500, 43000, 43500, 44000, 44500, 45000, 45500, 46000, 46500, 47000, 47500, 48000, 48500, 49000, 49500, 50000, 50500, 51000, 51500, 52000, 52500, 53000, 53500, 54000, 54500, 55000, 55500, 56000, 56500, 57000, 57500, 58000, 58500, 59000, 59500, 60000, 60500, 61000, 61500, 62000, 62500, 63000, 63500, 64000, 64500, 65000, 65500, 66000, 66500, 67000, 67500, 68000, 68500, 69000, 69500, 70000, 70500, 71000, 71500, 72000, 72500, 73000, 73500, 74000, 74500, 75000, 75500, 76000, 76500, 77000, 77500, 78000, 78500, 79000, 79500, 80000, 80500, 81000, 81500, 82000, 82500, 83000, 83500, 84000, 84500, 85000, 85500, 86000, 86500, 87000, 87500, 88000, 88500, 89000, 89500, 90000, 90500, 91000, 91500, 92000, 92500, 93000, 93500, 94000, 94500, 95000, 95500, 96000, 96500, 97000, 97500, 98000, 98500, 99000, 99500, 100000

There is a total of 200 numbers (up to 100000) that are divisible by 500.
The sum of these numbers is 10050000.
The arithmetic mean of these numbers is 50250.

How to find the numbers divisible by 500?

Finding all the numbers that can be divided by 500 is essentially the same as searching for the multiples of 500: if a number N is a multiple of 500, then 500 is a divisor of N.

Indeed, if we assume that N is a multiple of 500, this means there exists an integer k such that:

$k \times 500 = N$

Conversely, the result of N divided by 500 is this same integer k (without any remainder):

$k = \frac{N}{500}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 500 (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 500 less than 100000):

1 × 500 = 500
2 × 500 = 1000
3 × 500 = 1500
...
199 × 500 = 99500
200 × 500 = 100000