What are the numbers divisible by 825?

825, 1650, 2475, 3300, 4125, 4950, 5775, 6600, 7425, 8250, 9075, 9900, 10725, 11550, 12375, 13200, 14025, 14850, 15675, 16500, 17325, 18150, 18975, 19800, 20625, 21450, 22275, 23100, 23925, 24750, 25575, 26400, 27225, 28050, 28875, 29700, 30525, 31350, 32175, 33000, 33825, 34650, 35475, 36300, 37125, 37950, 38775, 39600, 40425, 41250, 42075, 42900, 43725, 44550, 45375, 46200, 47025, 47850, 48675, 49500, 50325, 51150, 51975, 52800, 53625, 54450, 55275, 56100, 56925, 57750, 58575, 59400, 60225, 61050, 61875, 62700, 63525, 64350, 65175, 66000, 66825, 67650, 68475, 69300, 70125, 70950, 71775, 72600, 73425, 74250, 75075, 75900, 76725, 77550, 78375, 79200, 80025, 80850, 81675, 82500, 83325, 84150, 84975, 85800, 86625, 87450, 88275, 89100, 89925, 90750, 91575, 92400, 93225, 94050, 94875, 95700, 96525, 97350, 98175, 99000, 99825

There is a total of 121 numbers (up to 100000) that are divisible by 825.
The sum of these numbers is 6089325.
The arithmetic mean of these numbers is 50325.

How to find the numbers divisible by 825?

Finding all the numbers that can be divided by 825 is essentially the same as searching for the multiples of 825: if a number N is a multiple of 825, then 825 is a divisor of N.

Indeed, if we assume that N is a multiple of 825, this means there exists an integer k such that:

$k \times 825 = N$

Conversely, the result of N divided by 825 is this same integer k (without any remainder):

$k = \frac{N}{825}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 825 (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 825 less than 100000):

1 × 825 = 825
2 × 825 = 1650
3 × 825 = 2475
...
120 × 825 = 99000
121 × 825 = 99825