What are the numbers divisible by 829?

829, 1658, 2487, 3316, 4145, 4974, 5803, 6632, 7461, 8290, 9119, 9948, 10777, 11606, 12435, 13264, 14093, 14922, 15751, 16580, 17409, 18238, 19067, 19896, 20725, 21554, 22383, 23212, 24041, 24870, 25699, 26528, 27357, 28186, 29015, 29844, 30673, 31502, 32331, 33160, 33989, 34818, 35647, 36476, 37305, 38134, 38963, 39792, 40621, 41450, 42279, 43108, 43937, 44766, 45595, 46424, 47253, 48082, 48911, 49740, 50569, 51398, 52227, 53056, 53885, 54714, 55543, 56372, 57201, 58030, 58859, 59688, 60517, 61346, 62175, 63004, 63833, 64662, 65491, 66320, 67149, 67978, 68807, 69636, 70465, 71294, 72123, 72952, 73781, 74610, 75439, 76268, 77097, 77926, 78755, 79584, 80413, 81242, 82071, 82900, 83729, 84558, 85387, 86216, 87045, 87874, 88703, 89532, 90361, 91190, 92019, 92848, 93677, 94506, 95335, 96164, 96993, 97822, 98651, 99480

There is a total of 120 numbers (up to 100000) that are divisible by 829.
The sum of these numbers is 6018540.
The arithmetic mean of these numbers is 50154.5.

How to find the numbers divisible by 829?

Finding all the numbers that can be divided by 829 is essentially the same as searching for the multiples of 829: if a number N is a multiple of 829, then 829 is a divisor of N.

Indeed, if we assume that N is a multiple of 829, this means there exists an integer k such that:

$k \times 829 = N$

Conversely, the result of N divided by 829 is this same integer k (without any remainder):

$k = \frac{N}{829}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 829 (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 829 less than 100000):

1 × 829 = 829
2 × 829 = 1658
3 × 829 = 2487
...
119 × 829 = 98651
120 × 829 = 99480