What are the numbers divisible by 5040?

5040, 10080, 15120, 20160, 25200, 30240, 35280, 40320, 45360, 50400, 55440, 60480, 65520, 70560, 75600, 80640, 85680, 90720, 95760

There is a total of 19 numbers (up to 100000) that are divisible by 5040.
The sum of these numbers is 957600.
The arithmetic mean of these numbers is 50400.

How to find the numbers divisible by 5040?

Finding all the numbers that can be divided by 5040 is essentially the same as searching for the multiples of 5040: if a number N is a multiple of 5040, then 5040 is a divisor of N.

Indeed, if we assume that N is a multiple of 5040, this means there exists an integer k such that:

$k \times 5040 = N$

Conversely, the result of N divided by 5040 is this same integer k (without any remainder):

$k = \frac{N}{5040}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 5040 (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 5040 less than 100000):

1 × 5040 = 5040
2 × 5040 = 10080
3 × 5040 = 15120
...
18 × 5040 = 90720
19 × 5040 = 95760