What are the numbers divisible by 429?

429, 858, 1287, 1716, 2145, 2574, 3003, 3432, 3861, 4290, 4719, 5148, 5577, 6006, 6435, 6864, 7293, 7722, 8151, 8580, 9009, 9438, 9867, 10296, 10725, 11154, 11583, 12012, 12441, 12870, 13299, 13728, 14157, 14586, 15015, 15444, 15873, 16302, 16731, 17160, 17589, 18018, 18447, 18876, 19305, 19734, 20163, 20592, 21021, 21450, 21879, 22308, 22737, 23166, 23595, 24024, 24453, 24882, 25311, 25740, 26169, 26598, 27027, 27456, 27885, 28314, 28743, 29172, 29601, 30030, 30459, 30888, 31317, 31746, 32175, 32604, 33033, 33462, 33891, 34320, 34749, 35178, 35607, 36036, 36465, 36894, 37323, 37752, 38181, 38610, 39039, 39468, 39897, 40326, 40755, 41184, 41613, 42042, 42471, 42900, 43329, 43758, 44187, 44616, 45045, 45474, 45903, 46332, 46761, 47190, 47619, 48048, 48477, 48906, 49335, 49764, 50193, 50622, 51051, 51480, 51909, 52338, 52767, 53196, 53625, 54054, 54483, 54912, 55341, 55770, 56199, 56628, 57057, 57486, 57915, 58344, 58773, 59202, 59631, 60060, 60489, 60918, 61347, 61776, 62205, 62634, 63063, 63492, 63921, 64350, 64779, 65208, 65637, 66066, 66495, 66924, 67353, 67782, 68211, 68640, 69069, 69498, 69927, 70356, 70785, 71214, 71643, 72072, 72501, 72930, 73359, 73788, 74217, 74646, 75075, 75504, 75933, 76362, 76791, 77220, 77649, 78078, 78507, 78936, 79365, 79794, 80223, 80652, 81081, 81510, 81939, 82368, 82797, 83226, 83655, 84084, 84513, 84942, 85371, 85800, 86229, 86658, 87087, 87516, 87945, 88374, 88803, 89232, 89661, 90090, 90519, 90948, 91377, 91806, 92235, 92664, 93093, 93522, 93951, 94380, 94809, 95238, 95667, 96096, 96525, 96954, 97383, 97812, 98241, 98670, 99099, 99528, 99957

There is a total of 233 numbers (up to 100000) that are divisible by 429.
The sum of these numbers is 11694969.
The arithmetic mean of these numbers is 50193.

How to find the numbers divisible by 429?

Finding all the numbers that can be divided by 429 is essentially the same as searching for the multiples of 429: if a number N is a multiple of 429, then 429 is a divisor of N.

Indeed, if we assume that N is a multiple of 429, this means there exists an integer k such that:

$k \times 429 = N$

Conversely, the result of N divided by 429 is this same integer k (without any remainder):

$k = \frac{N}{429}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 429 (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 429 less than 100000):

1 × 429 = 429
2 × 429 = 858
3 × 429 = 1287
...
232 × 429 = 99528
233 × 429 = 99957