Question

explain why the product of any four consecutive is divisible by 24

Answer 1

Let's pick a random number:
19

19 x 20 x 21 x 22 is the question, right?

20 is a factor of 4. There will always be 1 factor of 4.
21 is a factor of 3. There will always be 1 or 2 factors of 3.
22 is a factor of 2 (so is 20, btw). There will always be 2 factors of 2.
4 x 3 x 2 = 24.

Therefore, since there will always be a multiple of 4, a multiple of 3, and a multiple of 2 that is not a multiple of 4, you will have a multiple of 24.

To check, 19 x 20 x 21 x 22 = 175,560
175,560/24 = 7315. It works!

Answer 2

Thanks a million

Answer 3

you're welcome.