What are the numbers divisible by 735?

735, 1470, 2205, 2940, 3675, 4410, 5145, 5880, 6615, 7350, 8085, 8820, 9555, 10290, 11025, 11760, 12495, 13230, 13965, 14700, 15435, 16170, 16905, 17640, 18375, 19110, 19845, 20580, 21315, 22050, 22785, 23520, 24255, 24990, 25725, 26460, 27195, 27930, 28665, 29400, 30135, 30870, 31605, 32340, 33075, 33810, 34545, 35280, 36015, 36750, 37485, 38220, 38955, 39690, 40425, 41160, 41895, 42630, 43365, 44100, 44835, 45570, 46305, 47040, 47775, 48510, 49245, 49980, 50715, 51450, 52185, 52920, 53655, 54390, 55125, 55860, 56595, 57330, 58065, 58800, 59535, 60270, 61005, 61740, 62475, 63210, 63945, 64680, 65415, 66150, 66885, 67620, 68355, 69090, 69825, 70560, 71295, 72030, 72765, 73500, 74235, 74970, 75705, 76440, 77175, 77910, 78645, 79380, 80115, 80850, 81585, 82320, 83055, 83790, 84525, 85260, 85995, 86730, 87465, 88200, 88935, 89670, 90405, 91140, 91875, 92610, 93345, 94080, 94815, 95550, 96285, 97020, 97755, 98490, 99225, 99960

There is a total of 136 numbers (up to 100000) that are divisible by 735.
The sum of these numbers is 6847260.
The arithmetic mean of these numbers is 50347.5.

How to find the numbers divisible by 735?

Finding all the numbers that can be divided by 735 is essentially the same as searching for the multiples of 735: if a number N is a multiple of 735, then 735 is a divisor of N.

Indeed, if we assume that N is a multiple of 735, this means there exists an integer k such that:

$k \times 735 = N$

Conversely, the result of N divided by 735 is this same integer k (without any remainder):

$k = \frac{N}{735}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 735 (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 735 less than 100000):

1 × 735 = 735
2 × 735 = 1470
3 × 735 = 2205
...
135 × 735 = 99225
136 × 735 = 99960