What are the numbers divisible by 765?

765, 1530, 2295, 3060, 3825, 4590, 5355, 6120, 6885, 7650, 8415, 9180, 9945, 10710, 11475, 12240, 13005, 13770, 14535, 15300, 16065, 16830, 17595, 18360, 19125, 19890, 20655, 21420, 22185, 22950, 23715, 24480, 25245, 26010, 26775, 27540, 28305, 29070, 29835, 30600, 31365, 32130, 32895, 33660, 34425, 35190, 35955, 36720, 37485, 38250, 39015, 39780, 40545, 41310, 42075, 42840, 43605, 44370, 45135, 45900, 46665, 47430, 48195, 48960, 49725, 50490, 51255, 52020, 52785, 53550, 54315, 55080, 55845, 56610, 57375, 58140, 58905, 59670, 60435, 61200, 61965, 62730, 63495, 64260, 65025, 65790, 66555, 67320, 68085, 68850, 69615, 70380, 71145, 71910, 72675, 73440, 74205, 74970, 75735, 76500, 77265, 78030, 78795, 79560, 80325, 81090, 81855, 82620, 83385, 84150, 84915, 85680, 86445, 87210, 87975, 88740, 89505, 90270, 91035, 91800, 92565, 93330, 94095, 94860, 95625, 96390, 97155, 97920, 98685, 99450

There is a total of 130 numbers (up to 100000) that are divisible by 765.
The sum of these numbers is 6513975.
The arithmetic mean of these numbers is 50107.5.

How to find the numbers divisible by 765?

Finding all the numbers that can be divided by 765 is essentially the same as searching for the multiples of 765: if a number N is a multiple of 765, then 765 is a divisor of N.

Indeed, if we assume that N is a multiple of 765, this means there exists an integer k such that:

$k \times 765 = N$

Conversely, the result of N divided by 765 is this same integer k (without any remainder):

$k = \frac{N}{765}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 765 (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 765 less than 100000):

1 × 765 = 765
2 × 765 = 1530
3 × 765 = 2295
...
129 × 765 = 98685
130 × 765 = 99450