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intergers

by saadiagha » Fri Dec 21, 2012 11:50 am
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?
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by puneetkhurana2000 » Fri Dec 21, 2012 2:46 pm
The answer is 11 because f(24) contains 22(2*11) and 13 is not a possibility.
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by saadiagha » Fri Dec 21, 2012 2:51 pm
can I multiply 22.24, since they are the highest integers, and then factorize? Or will I be violating a principle doing that?
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by puneetkhurana2000 » Fri Dec 21, 2012 3:06 pm
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!!!
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