What are the numbers divisible by 585?

585, 1170, 1755, 2340, 2925, 3510, 4095, 4680, 5265, 5850, 6435, 7020, 7605, 8190, 8775, 9360, 9945, 10530, 11115, 11700, 12285, 12870, 13455, 14040, 14625, 15210, 15795, 16380, 16965, 17550, 18135, 18720, 19305, 19890, 20475, 21060, 21645, 22230, 22815, 23400, 23985, 24570, 25155, 25740, 26325, 26910, 27495, 28080, 28665, 29250, 29835, 30420, 31005, 31590, 32175, 32760, 33345, 33930, 34515, 35100, 35685, 36270, 36855, 37440, 38025, 38610, 39195, 39780, 40365, 40950, 41535, 42120, 42705, 43290, 43875, 44460, 45045, 45630, 46215, 46800, 47385, 47970, 48555, 49140, 49725, 50310, 50895, 51480, 52065, 52650, 53235, 53820, 54405, 54990, 55575, 56160, 56745, 57330, 57915, 58500, 59085, 59670, 60255, 60840, 61425, 62010, 62595, 63180, 63765, 64350, 64935, 65520, 66105, 66690, 67275, 67860, 68445, 69030, 69615, 70200, 70785, 71370, 71955, 72540, 73125, 73710, 74295, 74880, 75465, 76050, 76635, 77220, 77805, 78390, 78975, 79560, 80145, 80730, 81315, 81900, 82485, 83070, 83655, 84240, 84825, 85410, 85995, 86580, 87165, 87750, 88335, 88920, 89505, 90090, 90675, 91260, 91845, 92430, 93015, 93600, 94185, 94770, 95355, 95940, 96525, 97110, 97695, 98280, 98865, 99450

There is a total of 170 numbers (up to 100000) that are divisible by 585.
The sum of these numbers is 8502975.
The arithmetic mean of these numbers is 50017.5.

How to find the numbers divisible by 585?

Finding all the numbers that can be divided by 585 is essentially the same as searching for the multiples of 585: if a number N is a multiple of 585, then 585 is a divisor of N.

Indeed, if we assume that N is a multiple of 585, this means there exists an integer k such that:

$k \times 585 = N$

Conversely, the result of N divided by 585 is this same integer k (without any remainder):

$k = \frac{N}{585}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 585 (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 585 less than 100000):

1 × 585 = 585
2 × 585 = 1170
3 × 585 = 1755
...
169 × 585 = 98865
170 × 585 = 99450