What are the numbers divisible by 823?

823, 1646, 2469, 3292, 4115, 4938, 5761, 6584, 7407, 8230, 9053, 9876, 10699, 11522, 12345, 13168, 13991, 14814, 15637, 16460, 17283, 18106, 18929, 19752, 20575, 21398, 22221, 23044, 23867, 24690, 25513, 26336, 27159, 27982, 28805, 29628, 30451, 31274, 32097, 32920, 33743, 34566, 35389, 36212, 37035, 37858, 38681, 39504, 40327, 41150, 41973, 42796, 43619, 44442, 45265, 46088, 46911, 47734, 48557, 49380, 50203, 51026, 51849, 52672, 53495, 54318, 55141, 55964, 56787, 57610, 58433, 59256, 60079, 60902, 61725, 62548, 63371, 64194, 65017, 65840, 66663, 67486, 68309, 69132, 69955, 70778, 71601, 72424, 73247, 74070, 74893, 75716, 76539, 77362, 78185, 79008, 79831, 80654, 81477, 82300, 83123, 83946, 84769, 85592, 86415, 87238, 88061, 88884, 89707, 90530, 91353, 92176, 92999, 93822, 94645, 95468, 96291, 97114, 97937, 98760, 99583

There is a total of 121 numbers (up to 100000) that are divisible by 823.
The sum of these numbers is 6074563.
The arithmetic mean of these numbers is 50203.

How to find the numbers divisible by 823?

Finding all the numbers that can be divided by 823 is essentially the same as searching for the multiples of 823: if a number N is a multiple of 823, then 823 is a divisor of N.

Indeed, if we assume that N is a multiple of 823, this means there exists an integer k such that:

$k \times 823 = N$

Conversely, the result of N divided by 823 is this same integer k (without any remainder):

$k = \frac{N}{823}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 823 (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 823 less than 100000):

1 × 823 = 823
2 × 823 = 1646
3 × 823 = 2469
...
120 × 823 = 98760
121 × 823 = 99583