What are the numbers divisible by 725?

725, 1450, 2175, 2900, 3625, 4350, 5075, 5800, 6525, 7250, 7975, 8700, 9425, 10150, 10875, 11600, 12325, 13050, 13775, 14500, 15225, 15950, 16675, 17400, 18125, 18850, 19575, 20300, 21025, 21750, 22475, 23200, 23925, 24650, 25375, 26100, 26825, 27550, 28275, 29000, 29725, 30450, 31175, 31900, 32625, 33350, 34075, 34800, 35525, 36250, 36975, 37700, 38425, 39150, 39875, 40600, 41325, 42050, 42775, 43500, 44225, 44950, 45675, 46400, 47125, 47850, 48575, 49300, 50025, 50750, 51475, 52200, 52925, 53650, 54375, 55100, 55825, 56550, 57275, 58000, 58725, 59450, 60175, 60900, 61625, 62350, 63075, 63800, 64525, 65250, 65975, 66700, 67425, 68150, 68875, 69600, 70325, 71050, 71775, 72500, 73225, 73950, 74675, 75400, 76125, 76850, 77575, 78300, 79025, 79750, 80475, 81200, 81925, 82650, 83375, 84100, 84825, 85550, 86275, 87000, 87725, 88450, 89175, 89900, 90625, 91350, 92075, 92800, 93525, 94250, 94975, 95700, 96425, 97150, 97875, 98600, 99325

There is a total of 137 numbers (up to 100000) that are divisible by 725.
The sum of these numbers is 6853425.
The arithmetic mean of these numbers is 50025.

How to find the numbers divisible by 725?

Finding all the numbers that can be divided by 725 is essentially the same as searching for the multiples of 725: if a number N is a multiple of 725, then 725 is a divisor of N.

Indeed, if we assume that N is a multiple of 725, this means there exists an integer k such that:

$k \times 725 = N$

Conversely, the result of N divided by 725 is this same integer k (without any remainder):

$k = \frac{N}{725}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 725 (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 725 less than 100000):

1 × 725 = 725
2 × 725 = 1450
3 × 725 = 2175
...
136 × 725 = 98600
137 × 725 = 99325