What are the numbers divisible by 750?

750, 1500, 2250, 3000, 3750, 4500, 5250, 6000, 6750, 7500, 8250, 9000, 9750, 10500, 11250, 12000, 12750, 13500, 14250, 15000, 15750, 16500, 17250, 18000, 18750, 19500, 20250, 21000, 21750, 22500, 23250, 24000, 24750, 25500, 26250, 27000, 27750, 28500, 29250, 30000, 30750, 31500, 32250, 33000, 33750, 34500, 35250, 36000, 36750, 37500, 38250, 39000, 39750, 40500, 41250, 42000, 42750, 43500, 44250, 45000, 45750, 46500, 47250, 48000, 48750, 49500, 50250, 51000, 51750, 52500, 53250, 54000, 54750, 55500, 56250, 57000, 57750, 58500, 59250, 60000, 60750, 61500, 62250, 63000, 63750, 64500, 65250, 66000, 66750, 67500, 68250, 69000, 69750, 70500, 71250, 72000, 72750, 73500, 74250, 75000, 75750, 76500, 77250, 78000, 78750, 79500, 80250, 81000, 81750, 82500, 83250, 84000, 84750, 85500, 86250, 87000, 87750, 88500, 89250, 90000, 90750, 91500, 92250, 93000, 93750, 94500, 95250, 96000, 96750, 97500, 98250, 99000, 99750

There is a total of 133 numbers (up to 100000) that are divisible by 750.
The sum of these numbers is 6683250.
The arithmetic mean of these numbers is 50250.

How to find the numbers divisible by 750?

Finding all the numbers that can be divided by 750 is essentially the same as searching for the multiples of 750: if a number N is a multiple of 750, then 750 is a divisor of N.

Indeed, if we assume that N is a multiple of 750, this means there exists an integer k such that:

$k \times 750 = N$

Conversely, the result of N divided by 750 is this same integer k (without any remainder):

$k = \frac{N}{750}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 750 (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 750 less than 100000):

1 × 750 = 750
2 × 750 = 1500
3 × 750 = 2250
...
132 × 750 = 99000
133 × 750 = 99750