What are the numbers divisible by 820?

820, 1640, 2460, 3280, 4100, 4920, 5740, 6560, 7380, 8200, 9020, 9840, 10660, 11480, 12300, 13120, 13940, 14760, 15580, 16400, 17220, 18040, 18860, 19680, 20500, 21320, 22140, 22960, 23780, 24600, 25420, 26240, 27060, 27880, 28700, 29520, 30340, 31160, 31980, 32800, 33620, 34440, 35260, 36080, 36900, 37720, 38540, 39360, 40180, 41000, 41820, 42640, 43460, 44280, 45100, 45920, 46740, 47560, 48380, 49200, 50020, 50840, 51660, 52480, 53300, 54120, 54940, 55760, 56580, 57400, 58220, 59040, 59860, 60680, 61500, 62320, 63140, 63960, 64780, 65600, 66420, 67240, 68060, 68880, 69700, 70520, 71340, 72160, 72980, 73800, 74620, 75440, 76260, 77080, 77900, 78720, 79540, 80360, 81180, 82000, 82820, 83640, 84460, 85280, 86100, 86920, 87740, 88560, 89380, 90200, 91020, 91840, 92660, 93480, 94300, 95120, 95940, 96760, 97580, 98400, 99220

There is a total of 121 numbers (up to 100000) that are divisible by 820.
The sum of these numbers is 6052420.
The arithmetic mean of these numbers is 50020.

How to find the numbers divisible by 820?

Finding all the numbers that can be divided by 820 is essentially the same as searching for the multiples of 820: if a number N is a multiple of 820, then 820 is a divisor of N.

Indeed, if we assume that N is a multiple of 820, this means there exists an integer k such that:

$k \times 820 = N$

Conversely, the result of N divided by 820 is this same integer k (without any remainder):

$k = \frac{N}{820}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 820 (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 820 less than 100000):

1 × 820 = 820
2 × 820 = 1640
3 × 820 = 2460
...
120 × 820 = 98400
121 × 820 = 99220