What are the numbers divisible by 456?

456, 912, 1368, 1824, 2280, 2736, 3192, 3648, 4104, 4560, 5016, 5472, 5928, 6384, 6840, 7296, 7752, 8208, 8664, 9120, 9576, 10032, 10488, 10944, 11400, 11856, 12312, 12768, 13224, 13680, 14136, 14592, 15048, 15504, 15960, 16416, 16872, 17328, 17784, 18240, 18696, 19152, 19608, 20064, 20520, 20976, 21432, 21888, 22344, 22800, 23256, 23712, 24168, 24624, 25080, 25536, 25992, 26448, 26904, 27360, 27816, 28272, 28728, 29184, 29640, 30096, 30552, 31008, 31464, 31920, 32376, 32832, 33288, 33744, 34200, 34656, 35112, 35568, 36024, 36480, 36936, 37392, 37848, 38304, 38760, 39216, 39672, 40128, 40584, 41040, 41496, 41952, 42408, 42864, 43320, 43776, 44232, 44688, 45144, 45600, 46056, 46512, 46968, 47424, 47880, 48336, 48792, 49248, 49704, 50160, 50616, 51072, 51528, 51984, 52440, 52896, 53352, 53808, 54264, 54720, 55176, 55632, 56088, 56544, 57000, 57456, 57912, 58368, 58824, 59280, 59736, 60192, 60648, 61104, 61560, 62016, 62472, 62928, 63384, 63840, 64296, 64752, 65208, 65664, 66120, 66576, 67032, 67488, 67944, 68400, 68856, 69312, 69768, 70224, 70680, 71136, 71592, 72048, 72504, 72960, 73416, 73872, 74328, 74784, 75240, 75696, 76152, 76608, 77064, 77520, 77976, 78432, 78888, 79344, 79800, 80256, 80712, 81168, 81624, 82080, 82536, 82992, 83448, 83904, 84360, 84816, 85272, 85728, 86184, 86640, 87096, 87552, 88008, 88464, 88920, 89376, 89832, 90288, 90744, 91200, 91656, 92112, 92568, 93024, 93480, 93936, 94392, 94848, 95304, 95760, 96216, 96672, 97128, 97584, 98040, 98496, 98952, 99408, 99864

There is a total of 219 numbers (up to 100000) that are divisible by 456.
The sum of these numbers is 10985040.
The arithmetic mean of these numbers is 50160.

How to find the numbers divisible by 456?

Finding all the numbers that can be divided by 456 is essentially the same as searching for the multiples of 456: if a number N is a multiple of 456, then 456 is a divisor of N.

Indeed, if we assume that N is a multiple of 456, this means there exists an integer k such that:

$k \times 456 = N$

Conversely, the result of N divided by 456 is this same integer k (without any remainder):

$k = \frac{N}{456}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 456 (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 456 less than 100000):

1 × 456 = 456
2 × 456 = 912
3 × 456 = 1368
...
218 × 456 = 99408
219 × 456 = 99864