Hello guys,
I understand why 36 = n, and thus why Greg chose 12 and 36 as the correct answers, but I still do not understand why 72 cannot be n as well. If 72 = n, then n^2 = 5184 which it is a multiple of both 24 and 108.
So, Is 72 not a correct answers because then 24 (a divisor of 72) is not of divisor of 36 (which is also n)? Hope that makes sense.
Yes!
Yes 72 is a valid multiple!
In fact, this is the set S = {36, 72, 108, 144, 180, 216,…}
S is a multiple of an infinite set, BUT what numbers would guarantee the divisibility of every numbers in S? That has to be a 36, right?
So, Basically, all the factors of 36 would be the correct answers: {1, 2, 3, 6, 9, 12, 18, 36}
For example,
If you would divide the first five numbers of the set S by 9
You would get: {4, 8, 12, 16, 20}
See, the factors of 36 guarantee that divisibility, but 24 and 72 don’t.
Hope this helps!
Now it makes sense. Thank you!!!
