What are the numbers divisible by 821?

821, 1642, 2463, 3284, 4105, 4926, 5747, 6568, 7389, 8210, 9031, 9852, 10673, 11494, 12315, 13136, 13957, 14778, 15599, 16420, 17241, 18062, 18883, 19704, 20525, 21346, 22167, 22988, 23809, 24630, 25451, 26272, 27093, 27914, 28735, 29556, 30377, 31198, 32019, 32840, 33661, 34482, 35303, 36124, 36945, 37766, 38587, 39408, 40229, 41050, 41871, 42692, 43513, 44334, 45155, 45976, 46797, 47618, 48439, 49260, 50081, 50902, 51723, 52544, 53365, 54186, 55007, 55828, 56649, 57470, 58291, 59112, 59933, 60754, 61575, 62396, 63217, 64038, 64859, 65680, 66501, 67322, 68143, 68964, 69785, 70606, 71427, 72248, 73069, 73890, 74711, 75532, 76353, 77174, 77995, 78816, 79637, 80458, 81279, 82100, 82921, 83742, 84563, 85384, 86205, 87026, 87847, 88668, 89489, 90310, 91131, 91952, 92773, 93594, 94415, 95236, 96057, 96878, 97699, 98520, 99341

There is a total of 121 numbers (up to 100000) that are divisible by 821.
The sum of these numbers is 6059801.
The arithmetic mean of these numbers is 50081.

How to find the numbers divisible by 821?

Finding all the numbers that can be divided by 821 is essentially the same as searching for the multiples of 821: if a number N is a multiple of 821, then 821 is a divisor of N.

Indeed, if we assume that N is a multiple of 821, this means there exists an integer k such that:

$k \times 821 = N$

Conversely, the result of N divided by 821 is this same integer k (without any remainder):

$k = \frac{N}{821}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 821 (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 821 less than 100000):

1 × 821 = 821
2 × 821 = 1642
3 × 821 = 2463
...
120 × 821 = 98520
121 × 821 = 99341