What are the numbers divisible by 975?

975, 1950, 2925, 3900, 4875, 5850, 6825, 7800, 8775, 9750, 10725, 11700, 12675, 13650, 14625, 15600, 16575, 17550, 18525, 19500, 20475, 21450, 22425, 23400, 24375, 25350, 26325, 27300, 28275, 29250, 30225, 31200, 32175, 33150, 34125, 35100, 36075, 37050, 38025, 39000, 39975, 40950, 41925, 42900, 43875, 44850, 45825, 46800, 47775, 48750, 49725, 50700, 51675, 52650, 53625, 54600, 55575, 56550, 57525, 58500, 59475, 60450, 61425, 62400, 63375, 64350, 65325, 66300, 67275, 68250, 69225, 70200, 71175, 72150, 73125, 74100, 75075, 76050, 77025, 78000, 78975, 79950, 80925, 81900, 82875, 83850, 84825, 85800, 86775, 87750, 88725, 89700, 90675, 91650, 92625, 93600, 94575, 95550, 96525, 97500, 98475, 99450

There is a total of 102 numbers (up to 100000) that are divisible by 975.
The sum of these numbers is 5121675.
The arithmetic mean of these numbers is 50212.5.

How to find the numbers divisible by 975?

Finding all the numbers that can be divided by 975 is essentially the same as searching for the multiples of 975: if a number N is a multiple of 975, then 975 is a divisor of N.

Indeed, if we assume that N is a multiple of 975, this means there exists an integer k such that:

$k \times 975 = N$

Conversely, the result of N divided by 975 is this same integer k (without any remainder):

$k = \frac{N}{975}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 975 (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 975 less than 100000):

1 × 975 = 975
2 × 975 = 1950
3 × 975 = 2925
...
101 × 975 = 98475
102 × 975 = 99450