GMAT Number Properties: What is the greatest prime factor…

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 \times 4 \times 6 \times 8 \times 10 \times 12 . What is the greatest prime factor of f (24) ?

number theoryprime factorizationodds/evens

Explanation	Calculations	Help
$We factor each even term from 2 to 24 as 2 times an integer, then collect the powers of 2 and the remaining product.$	$f (24) = 2 \times 4 \times 6 \times 8 \times 10 \times 12 \times 14 \times 16 \times 18 \times 20 \times 22 \times 24 = 2^{12} \times (1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10 \times 11 \times 12) = 2^{12} \times 12!$
$We break down 12! into prime powers to find its highest prime factor.$	$12! = 2^{10} \times 3^{5} \times 5^{2} \times 7 \times 11 The greatest prime factor is 11$

11 (E)

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