What are the numbers divisible by 1027?

1027, 2054, 3081, 4108, 5135, 6162, 7189, 8216, 9243, 10270, 11297, 12324, 13351, 14378, 15405, 16432, 17459, 18486, 19513, 20540, 21567, 22594, 23621, 24648, 25675, 26702, 27729, 28756, 29783, 30810, 31837, 32864, 33891, 34918, 35945, 36972, 37999, 39026, 40053, 41080, 42107, 43134, 44161, 45188, 46215, 47242, 48269, 49296, 50323, 51350, 52377, 53404, 54431, 55458, 56485, 57512, 58539, 59566, 60593, 61620, 62647, 63674, 64701, 65728, 66755, 67782, 68809, 69836, 70863, 71890, 72917, 73944, 74971, 75998, 77025, 78052, 79079, 80106, 81133, 82160, 83187, 84214, 85241, 86268, 87295, 88322, 89349, 90376, 91403, 92430, 93457, 94484, 95511, 96538, 97565, 98592, 99619

There is a total of 97 numbers (up to 100000) that are divisible by 1027.
The sum of these numbers is 4881331.
The arithmetic mean of these numbers is 50323.

How to find the numbers divisible by 1027?

Finding all the numbers that can be divided by 1027 is essentially the same as searching for the multiples of 1027: if a number N is a multiple of 1027, then 1027 is a divisor of N.

Indeed, if we assume that N is a multiple of 1027, this means there exists an integer k such that:

$k \times 1027 = N$

Conversely, the result of N divided by 1027 is this same integer k (without any remainder):

$k = \frac{N}{1027}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 1027 (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 1027 less than 100000):

1 × 1027 = 1027
2 × 1027 = 2054
3 × 1027 = 3081
...
96 × 1027 = 98592
97 × 1027 = 99619