What are the numbers divisible by 1008?

1008, 2016, 3024, 4032, 5040, 6048, 7056, 8064, 9072, 10080, 11088, 12096, 13104, 14112, 15120, 16128, 17136, 18144, 19152, 20160, 21168, 22176, 23184, 24192, 25200, 26208, 27216, 28224, 29232, 30240, 31248, 32256, 33264, 34272, 35280, 36288, 37296, 38304, 39312, 40320, 41328, 42336, 43344, 44352, 45360, 46368, 47376, 48384, 49392, 50400, 51408, 52416, 53424, 54432, 55440, 56448, 57456, 58464, 59472, 60480, 61488, 62496, 63504, 64512, 65520, 66528, 67536, 68544, 69552, 70560, 71568, 72576, 73584, 74592, 75600, 76608, 77616, 78624, 79632, 80640, 81648, 82656, 83664, 84672, 85680, 86688, 87696, 88704, 89712, 90720, 91728, 92736, 93744, 94752, 95760, 96768, 97776, 98784, 99792

There is a total of 99 numbers (up to 100000) that are divisible by 1008.
The sum of these numbers is 4989600.
The arithmetic mean of these numbers is 50400.

How to find the numbers divisible by 1008?

Finding all the numbers that can be divided by 1008 is essentially the same as searching for the multiples of 1008: if a number N is a multiple of 1008, then 1008 is a divisor of N.

Indeed, if we assume that N is a multiple of 1008, this means there exists an integer k such that:

$k \times 1008 = N$

Conversely, the result of N divided by 1008 is this same integer k (without any remainder):

$k = \frac{N}{1008}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 1008 (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 1008 less than 100000):

1 × 1008 = 1008
2 × 1008 = 2016
3 × 1008 = 3024
...
98 × 1008 = 98784
99 × 1008 = 99792