What are the numbers divisible by 1050?

1050, 2100, 3150, 4200, 5250, 6300, 7350, 8400, 9450, 10500, 11550, 12600, 13650, 14700, 15750, 16800, 17850, 18900, 19950, 21000, 22050, 23100, 24150, 25200, 26250, 27300, 28350, 29400, 30450, 31500, 32550, 33600, 34650, 35700, 36750, 37800, 38850, 39900, 40950, 42000, 43050, 44100, 45150, 46200, 47250, 48300, 49350, 50400, 51450, 52500, 53550, 54600, 55650, 56700, 57750, 58800, 59850, 60900, 61950, 63000, 64050, 65100, 66150, 67200, 68250, 69300, 70350, 71400, 72450, 73500, 74550, 75600, 76650, 77700, 78750, 79800, 80850, 81900, 82950, 84000, 85050, 86100, 87150, 88200, 89250, 90300, 91350, 92400, 93450, 94500, 95550, 96600, 97650, 98700, 99750

There is a total of 95 numbers (up to 100000) that are divisible by 1050.
The sum of these numbers is 4788000.
The arithmetic mean of these numbers is 50400.

How to find the numbers divisible by 1050?

Finding all the numbers that can be divided by 1050 is essentially the same as searching for the multiples of 1050: if a number N is a multiple of 1050, then 1050 is a divisor of N.

Indeed, if we assume that N is a multiple of 1050, this means there exists an integer k such that:

$k \times 1050 = N$

Conversely, the result of N divided by 1050 is this same integer k (without any remainder):

$k = \frac{N}{1050}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 1050 (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 1050 less than 100000):

1 × 1050 = 1050
2 × 1050 = 2100
3 × 1050 = 3150
...
94 × 1050 = 98700
95 × 1050 = 99750