Problem Solving

For every even positive integer m,f(m)represents the product of all even integers from 2 to m inclusive. for example f(12)= 2.4.6.8.10.12
What is the greatest prime factor of f(24)

I got the correct answer but my working was different. Any ideas if there is more than one correct way of answering this?

The answer is 11 because f(24) contains 22(2*11) and 13 is not a possibility.

can I multiply 22.24, since they are the highest integers, and then factorize? Or will I be violating a principle doing that?

There is no need to do that because even after multiplication and then factorization as suggested by you the greatest prime factor will be 11 only.

So, I don't see a point.

E.g.
Greatest prime factor of 1*2*3 is 3
or
Greatest prime factor of 6 (which has 1,2,3,6 as factors) is also 3.

Hope this makes sense!!!