What are the numbers divisible by 405?

405, 810, 1215, 1620, 2025, 2430, 2835, 3240, 3645, 4050, 4455, 4860, 5265, 5670, 6075, 6480, 6885, 7290, 7695, 8100, 8505, 8910, 9315, 9720, 10125, 10530, 10935, 11340, 11745, 12150, 12555, 12960, 13365, 13770, 14175, 14580, 14985, 15390, 15795, 16200, 16605, 17010, 17415, 17820, 18225, 18630, 19035, 19440, 19845, 20250, 20655, 21060, 21465, 21870, 22275, 22680, 23085, 23490, 23895, 24300, 24705, 25110, 25515, 25920, 26325, 26730, 27135, 27540, 27945, 28350, 28755, 29160, 29565, 29970, 30375, 30780, 31185, 31590, 31995, 32400, 32805, 33210, 33615, 34020, 34425, 34830, 35235, 35640, 36045, 36450, 36855, 37260, 37665, 38070, 38475, 38880, 39285, 39690, 40095, 40500, 40905, 41310, 41715, 42120, 42525, 42930, 43335, 43740, 44145, 44550, 44955, 45360, 45765, 46170, 46575, 46980, 47385, 47790, 48195, 48600, 49005, 49410, 49815, 50220, 50625, 51030, 51435, 51840, 52245, 52650, 53055, 53460, 53865, 54270, 54675, 55080, 55485, 55890, 56295, 56700, 57105, 57510, 57915, 58320, 58725, 59130, 59535, 59940, 60345, 60750, 61155, 61560, 61965, 62370, 62775, 63180, 63585, 63990, 64395, 64800, 65205, 65610, 66015, 66420, 66825, 67230, 67635, 68040, 68445, 68850, 69255, 69660, 70065, 70470, 70875, 71280, 71685, 72090, 72495, 72900, 73305, 73710, 74115, 74520, 74925, 75330, 75735, 76140, 76545, 76950, 77355, 77760, 78165, 78570, 78975, 79380, 79785, 80190, 80595, 81000, 81405, 81810, 82215, 82620, 83025, 83430, 83835, 84240, 84645, 85050, 85455, 85860, 86265, 86670, 87075, 87480, 87885, 88290, 88695, 89100, 89505, 89910, 90315, 90720, 91125, 91530, 91935, 92340, 92745, 93150, 93555, 93960, 94365, 94770, 95175, 95580, 95985, 96390, 96795, 97200, 97605, 98010, 98415, 98820, 99225, 99630

There is a total of 246 numbers (up to 100000) that are divisible by 405.
The sum of these numbers is 12304305.
The arithmetic mean of these numbers is 50017.5.

How to find the numbers divisible by 405?

Finding all the numbers that can be divided by 405 is essentially the same as searching for the multiples of 405: if a number N is a multiple of 405, then 405 is a divisor of N.

Indeed, if we assume that N is a multiple of 405, this means there exists an integer k such that:

$k \times 405 = N$

Conversely, the result of N divided by 405 is this same integer k (without any remainder):

$k = \frac{N}{405}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 405 (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 405 less than 100000):

1 × 405 = 405
2 × 405 = 810
3 × 405 = 1215
...
245 × 405 = 99225
246 × 405 = 99630