What are the numbers divisible by 420?

420, 840, 1260, 1680, 2100, 2520, 2940, 3360, 3780, 4200, 4620, 5040, 5460, 5880, 6300, 6720, 7140, 7560, 7980, 8400, 8820, 9240, 9660, 10080, 10500, 10920, 11340, 11760, 12180, 12600, 13020, 13440, 13860, 14280, 14700, 15120, 15540, 15960, 16380, 16800, 17220, 17640, 18060, 18480, 18900, 19320, 19740, 20160, 20580, 21000, 21420, 21840, 22260, 22680, 23100, 23520, 23940, 24360, 24780, 25200, 25620, 26040, 26460, 26880, 27300, 27720, 28140, 28560, 28980, 29400, 29820, 30240, 30660, 31080, 31500, 31920, 32340, 32760, 33180, 33600, 34020, 34440, 34860, 35280, 35700, 36120, 36540, 36960, 37380, 37800, 38220, 38640, 39060, 39480, 39900, 40320, 40740, 41160, 41580, 42000, 42420, 42840, 43260, 43680, 44100, 44520, 44940, 45360, 45780, 46200, 46620, 47040, 47460, 47880, 48300, 48720, 49140, 49560, 49980, 50400, 50820, 51240, 51660, 52080, 52500, 52920, 53340, 53760, 54180, 54600, 55020, 55440, 55860, 56280, 56700, 57120, 57540, 57960, 58380, 58800, 59220, 59640, 60060, 60480, 60900, 61320, 61740, 62160, 62580, 63000, 63420, 63840, 64260, 64680, 65100, 65520, 65940, 66360, 66780, 67200, 67620, 68040, 68460, 68880, 69300, 69720, 70140, 70560, 70980, 71400, 71820, 72240, 72660, 73080, 73500, 73920, 74340, 74760, 75180, 75600, 76020, 76440, 76860, 77280, 77700, 78120, 78540, 78960, 79380, 79800, 80220, 80640, 81060, 81480, 81900, 82320, 82740, 83160, 83580, 84000, 84420, 84840, 85260, 85680, 86100, 86520, 86940, 87360, 87780, 88200, 88620, 89040, 89460, 89880, 90300, 90720, 91140, 91560, 91980, 92400, 92820, 93240, 93660, 94080, 94500, 94920, 95340, 95760, 96180, 96600, 97020, 97440, 97860, 98280, 98700, 99120, 99540, 99960

There is a total of 238 numbers (up to 100000) that are divisible by 420.
The sum of these numbers is 11945220.
The arithmetic mean of these numbers is 50190.

How to find the numbers divisible by 420?

Finding all the numbers that can be divided by 420 is essentially the same as searching for the multiples of 420: if a number N is a multiple of 420, then 420 is a divisor of N.

Indeed, if we assume that N is a multiple of 420, this means there exists an integer k such that:

$k \times 420 = N$

Conversely, the result of N divided by 420 is this same integer k (without any remainder):

$k = \frac{N}{420}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 420 (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 420 less than 100000):

1 × 420 = 420
2 × 420 = 840
3 × 420 = 1260
...
237 × 420 = 99540
238 × 420 = 99960