What are the numbers divisible by 705?

705, 1410, 2115, 2820, 3525, 4230, 4935, 5640, 6345, 7050, 7755, 8460, 9165, 9870, 10575, 11280, 11985, 12690, 13395, 14100, 14805, 15510, 16215, 16920, 17625, 18330, 19035, 19740, 20445, 21150, 21855, 22560, 23265, 23970, 24675, 25380, 26085, 26790, 27495, 28200, 28905, 29610, 30315, 31020, 31725, 32430, 33135, 33840, 34545, 35250, 35955, 36660, 37365, 38070, 38775, 39480, 40185, 40890, 41595, 42300, 43005, 43710, 44415, 45120, 45825, 46530, 47235, 47940, 48645, 49350, 50055, 50760, 51465, 52170, 52875, 53580, 54285, 54990, 55695, 56400, 57105, 57810, 58515, 59220, 59925, 60630, 61335, 62040, 62745, 63450, 64155, 64860, 65565, 66270, 66975, 67680, 68385, 69090, 69795, 70500, 71205, 71910, 72615, 73320, 74025, 74730, 75435, 76140, 76845, 77550, 78255, 78960, 79665, 80370, 81075, 81780, 82485, 83190, 83895, 84600, 85305, 86010, 86715, 87420, 88125, 88830, 89535, 90240, 90945, 91650, 92355, 93060, 93765, 94470, 95175, 95880, 96585, 97290, 97995, 98700, 99405

There is a total of 141 numbers (up to 100000) that are divisible by 705.
The sum of these numbers is 7057755.
The arithmetic mean of these numbers is 50055.

How to find the numbers divisible by 705?

Finding all the numbers that can be divided by 705 is essentially the same as searching for the multiples of 705: if a number N is a multiple of 705, then 705 is a divisor of N.

Indeed, if we assume that N is a multiple of 705, this means there exists an integer k such that:

$k \times 705 = N$

Conversely, the result of N divided by 705 is this same integer k (without any remainder):

$k = \frac{N}{705}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 705 (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 705 less than 100000):

1 × 705 = 705
2 × 705 = 1410
3 × 705 = 2115
...
140 × 705 = 98700
141 × 705 = 99405