What are the numbers divisible by 525?

525, 1050, 1575, 2100, 2625, 3150, 3675, 4200, 4725, 5250, 5775, 6300, 6825, 7350, 7875, 8400, 8925, 9450, 9975, 10500, 11025, 11550, 12075, 12600, 13125, 13650, 14175, 14700, 15225, 15750, 16275, 16800, 17325, 17850, 18375, 18900, 19425, 19950, 20475, 21000, 21525, 22050, 22575, 23100, 23625, 24150, 24675, 25200, 25725, 26250, 26775, 27300, 27825, 28350, 28875, 29400, 29925, 30450, 30975, 31500, 32025, 32550, 33075, 33600, 34125, 34650, 35175, 35700, 36225, 36750, 37275, 37800, 38325, 38850, 39375, 39900, 40425, 40950, 41475, 42000, 42525, 43050, 43575, 44100, 44625, 45150, 45675, 46200, 46725, 47250, 47775, 48300, 48825, 49350, 49875, 50400, 50925, 51450, 51975, 52500, 53025, 53550, 54075, 54600, 55125, 55650, 56175, 56700, 57225, 57750, 58275, 58800, 59325, 59850, 60375, 60900, 61425, 61950, 62475, 63000, 63525, 64050, 64575, 65100, 65625, 66150, 66675, 67200, 67725, 68250, 68775, 69300, 69825, 70350, 70875, 71400, 71925, 72450, 72975, 73500, 74025, 74550, 75075, 75600, 76125, 76650, 77175, 77700, 78225, 78750, 79275, 79800, 80325, 80850, 81375, 81900, 82425, 82950, 83475, 84000, 84525, 85050, 85575, 86100, 86625, 87150, 87675, 88200, 88725, 89250, 89775, 90300, 90825, 91350, 91875, 92400, 92925, 93450, 93975, 94500, 95025, 95550, 96075, 96600, 97125, 97650, 98175, 98700, 99225, 99750

There is a total of 190 numbers (up to 100000) that are divisible by 525.
The sum of these numbers is 9526125.
The arithmetic mean of these numbers is 50137.5.

How to find the numbers divisible by 525?

Finding all the numbers that can be divided by 525 is essentially the same as searching for the multiples of 525: if a number N is a multiple of 525, then 525 is a divisor of N.

Indeed, if we assume that N is a multiple of 525, this means there exists an integer k such that:

$k \times 525 = N$

Conversely, the result of N divided by 525 is this same integer k (without any remainder):

$k = \frac{N}{525}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 525 (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 525 less than 100000):

1 × 525 = 525
2 × 525 = 1050
3 × 525 = 1575
...
189 × 525 = 99225
190 × 525 = 99750