What are the numbers divisible by 390?

390, 780, 1170, 1560, 1950, 2340, 2730, 3120, 3510, 3900, 4290, 4680, 5070, 5460, 5850, 6240, 6630, 7020, 7410, 7800, 8190, 8580, 8970, 9360, 9750, 10140, 10530, 10920, 11310, 11700, 12090, 12480, 12870, 13260, 13650, 14040, 14430, 14820, 15210, 15600, 15990, 16380, 16770, 17160, 17550, 17940, 18330, 18720, 19110, 19500, 19890, 20280, 20670, 21060, 21450, 21840, 22230, 22620, 23010, 23400, 23790, 24180, 24570, 24960, 25350, 25740, 26130, 26520, 26910, 27300, 27690, 28080, 28470, 28860, 29250, 29640, 30030, 30420, 30810, 31200, 31590, 31980, 32370, 32760, 33150, 33540, 33930, 34320, 34710, 35100, 35490, 35880, 36270, 36660, 37050, 37440, 37830, 38220, 38610, 39000, 39390, 39780, 40170, 40560, 40950, 41340, 41730, 42120, 42510, 42900, 43290, 43680, 44070, 44460, 44850, 45240, 45630, 46020, 46410, 46800, 47190, 47580, 47970, 48360, 48750, 49140, 49530, 49920, 50310, 50700, 51090, 51480, 51870, 52260, 52650, 53040, 53430, 53820, 54210, 54600, 54990, 55380, 55770, 56160, 56550, 56940, 57330, 57720, 58110, 58500, 58890, 59280, 59670, 60060, 60450, 60840, 61230, 61620, 62010, 62400, 62790, 63180, 63570, 63960, 64350, 64740, 65130, 65520, 65910, 66300, 66690, 67080, 67470, 67860, 68250, 68640, 69030, 69420, 69810, 70200, 70590, 70980, 71370, 71760, 72150, 72540, 72930, 73320, 73710, 74100, 74490, 74880, 75270, 75660, 76050, 76440, 76830, 77220, 77610, 78000, 78390, 78780, 79170, 79560, 79950, 80340, 80730, 81120, 81510, 81900, 82290, 82680, 83070, 83460, 83850, 84240, 84630, 85020, 85410, 85800, 86190, 86580, 86970, 87360, 87750, 88140, 88530, 88920, 89310, 89700, 90090, 90480, 90870, 91260, 91650, 92040, 92430, 92820, 93210, 93600, 93990, 94380, 94770, 95160, 95550, 95940, 96330, 96720, 97110, 97500, 97890, 98280, 98670, 99060, 99450, 99840

There is a total of 256 numbers (up to 100000) that are divisible by 390.
The sum of these numbers is 12829440.
The arithmetic mean of these numbers is 50115.

How to find the numbers divisible by 390?

Finding all the numbers that can be divided by 390 is essentially the same as searching for the multiples of 390: if a number N is a multiple of 390, then 390 is a divisor of N.

Indeed, if we assume that N is a multiple of 390, this means there exists an integer k such that:

$k \times 390 = N$

Conversely, the result of N divided by 390 is this same integer k (without any remainder):

$k = \frac{N}{390}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 390 (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 390 less than 100000):

1 × 390 = 390
2 × 390 = 780
3 × 390 = 1170
...
255 × 390 = 99450
256 × 390 = 99840