What are the numbers divisible by 415?

415, 830, 1245, 1660, 2075, 2490, 2905, 3320, 3735, 4150, 4565, 4980, 5395, 5810, 6225, 6640, 7055, 7470, 7885, 8300, 8715, 9130, 9545, 9960, 10375, 10790, 11205, 11620, 12035, 12450, 12865, 13280, 13695, 14110, 14525, 14940, 15355, 15770, 16185, 16600, 17015, 17430, 17845, 18260, 18675, 19090, 19505, 19920, 20335, 20750, 21165, 21580, 21995, 22410, 22825, 23240, 23655, 24070, 24485, 24900, 25315, 25730, 26145, 26560, 26975, 27390, 27805, 28220, 28635, 29050, 29465, 29880, 30295, 30710, 31125, 31540, 31955, 32370, 32785, 33200, 33615, 34030, 34445, 34860, 35275, 35690, 36105, 36520, 36935, 37350, 37765, 38180, 38595, 39010, 39425, 39840, 40255, 40670, 41085, 41500, 41915, 42330, 42745, 43160, 43575, 43990, 44405, 44820, 45235, 45650, 46065, 46480, 46895, 47310, 47725, 48140, 48555, 48970, 49385, 49800, 50215, 50630, 51045, 51460, 51875, 52290, 52705, 53120, 53535, 53950, 54365, 54780, 55195, 55610, 56025, 56440, 56855, 57270, 57685, 58100, 58515, 58930, 59345, 59760, 60175, 60590, 61005, 61420, 61835, 62250, 62665, 63080, 63495, 63910, 64325, 64740, 65155, 65570, 65985, 66400, 66815, 67230, 67645, 68060, 68475, 68890, 69305, 69720, 70135, 70550, 70965, 71380, 71795, 72210, 72625, 73040, 73455, 73870, 74285, 74700, 75115, 75530, 75945, 76360, 76775, 77190, 77605, 78020, 78435, 78850, 79265, 79680, 80095, 80510, 80925, 81340, 81755, 82170, 82585, 83000, 83415, 83830, 84245, 84660, 85075, 85490, 85905, 86320, 86735, 87150, 87565, 87980, 88395, 88810, 89225, 89640, 90055, 90470, 90885, 91300, 91715, 92130, 92545, 92960, 93375, 93790, 94205, 94620, 95035, 95450, 95865, 96280, 96695, 97110, 97525, 97940, 98355, 98770, 99185, 99600

There is a total of 240 numbers (up to 100000) that are divisible by 415.
The sum of these numbers is 12001800.
The arithmetic mean of these numbers is 50007.5.

How to find the numbers divisible by 415?

Finding all the numbers that can be divided by 415 is essentially the same as searching for the multiples of 415: if a number N is a multiple of 415, then 415 is a divisor of N.

Indeed, if we assume that N is a multiple of 415, this means there exists an integer k such that:

$k \times 415 = N$

Conversely, the result of N divided by 415 is this same integer k (without any remainder):

$k = \frac{N}{415}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 415 (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 415 less than 100000):

1 × 415 = 415
2 × 415 = 830
3 × 415 = 1245
...
239 × 415 = 99185
240 × 415 = 99600