What are the numbers divisible by 1029?

1029, 2058, 3087, 4116, 5145, 6174, 7203, 8232, 9261, 10290, 11319, 12348, 13377, 14406, 15435, 16464, 17493, 18522, 19551, 20580, 21609, 22638, 23667, 24696, 25725, 26754, 27783, 28812, 29841, 30870, 31899, 32928, 33957, 34986, 36015, 37044, 38073, 39102, 40131, 41160, 42189, 43218, 44247, 45276, 46305, 47334, 48363, 49392, 50421, 51450, 52479, 53508, 54537, 55566, 56595, 57624, 58653, 59682, 60711, 61740, 62769, 63798, 64827, 65856, 66885, 67914, 68943, 69972, 71001, 72030, 73059, 74088, 75117, 76146, 77175, 78204, 79233, 80262, 81291, 82320, 83349, 84378, 85407, 86436, 87465, 88494, 89523, 90552, 91581, 92610, 93639, 94668, 95697, 96726, 97755, 98784, 99813

There is a total of 97 numbers (up to 100000) that are divisible by 1029.
The sum of these numbers is 4890837.
The arithmetic mean of these numbers is 50421.

How to find the numbers divisible by 1029?

Finding all the numbers that can be divided by 1029 is essentially the same as searching for the multiples of 1029: if a number N is a multiple of 1029, then 1029 is a divisor of N.

Indeed, if we assume that N is a multiple of 1029, this means there exists an integer k such that:

$k \times 1029 = N$

Conversely, the result of N divided by 1029 is this same integer k (without any remainder):

$k = \frac{N}{1029}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 1029 (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 1029 less than 100000):

1 × 1029 = 1029
2 × 1029 = 2058
3 × 1029 = 3087
...
96 × 1029 = 98784
97 × 1029 = 99813