What are the numbers divisible by 1038?

1038, 2076, 3114, 4152, 5190, 6228, 7266, 8304, 9342, 10380, 11418, 12456, 13494, 14532, 15570, 16608, 17646, 18684, 19722, 20760, 21798, 22836, 23874, 24912, 25950, 26988, 28026, 29064, 30102, 31140, 32178, 33216, 34254, 35292, 36330, 37368, 38406, 39444, 40482, 41520, 42558, 43596, 44634, 45672, 46710, 47748, 48786, 49824, 50862, 51900, 52938, 53976, 55014, 56052, 57090, 58128, 59166, 60204, 61242, 62280, 63318, 64356, 65394, 66432, 67470, 68508, 69546, 70584, 71622, 72660, 73698, 74736, 75774, 76812, 77850, 78888, 79926, 80964, 82002, 83040, 84078, 85116, 86154, 87192, 88230, 89268, 90306, 91344, 92382, 93420, 94458, 95496, 96534, 97572, 98610, 99648

There is a total of 96 numbers (up to 100000) that are divisible by 1038.
The sum of these numbers is 4832928.
The arithmetic mean of these numbers is 50343.

How to find the numbers divisible by 1038?

Finding all the numbers that can be divided by 1038 is essentially the same as searching for the multiples of 1038: if a number N is a multiple of 1038, then 1038 is a divisor of N.

Indeed, if we assume that N is a multiple of 1038, this means there exists an integer k such that:

$k \times 1038 = N$

Conversely, the result of N divided by 1038 is this same integer k (without any remainder):

$k = \frac{N}{1038}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 1038 (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 1038 less than 100000):

1 × 1038 = 1038
2 × 1038 = 2076
3 × 1038 = 3114
...
95 × 1038 = 98610
96 × 1038 = 99648