What are the numbers divisible by 789?

789, 1578, 2367, 3156, 3945, 4734, 5523, 6312, 7101, 7890, 8679, 9468, 10257, 11046, 11835, 12624, 13413, 14202, 14991, 15780, 16569, 17358, 18147, 18936, 19725, 20514, 21303, 22092, 22881, 23670, 24459, 25248, 26037, 26826, 27615, 28404, 29193, 29982, 30771, 31560, 32349, 33138, 33927, 34716, 35505, 36294, 37083, 37872, 38661, 39450, 40239, 41028, 41817, 42606, 43395, 44184, 44973, 45762, 46551, 47340, 48129, 48918, 49707, 50496, 51285, 52074, 52863, 53652, 54441, 55230, 56019, 56808, 57597, 58386, 59175, 59964, 60753, 61542, 62331, 63120, 63909, 64698, 65487, 66276, 67065, 67854, 68643, 69432, 70221, 71010, 71799, 72588, 73377, 74166, 74955, 75744, 76533, 77322, 78111, 78900, 79689, 80478, 81267, 82056, 82845, 83634, 84423, 85212, 86001, 86790, 87579, 88368, 89157, 89946, 90735, 91524, 92313, 93102, 93891, 94680, 95469, 96258, 97047, 97836, 98625, 99414

There is a total of 126 numbers (up to 100000) that are divisible by 789.
The sum of these numbers is 6312789.
The arithmetic mean of these numbers is 50101.5.

How to find the numbers divisible by 789?

Finding all the numbers that can be divided by 789 is essentially the same as searching for the multiples of 789: if a number N is a multiple of 789, then 789 is a divisor of N.

Indeed, if we assume that N is a multiple of 789, this means there exists an integer k such that:

$k \times 789 = N$

Conversely, the result of N divided by 789 is this same integer k (without any remainder):

$k = \frac{N}{789}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 789 (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 789 less than 100000):

1 × 789 = 789
2 × 789 = 1578
3 × 789 = 2367
...
125 × 789 = 98625
126 × 789 = 99414