For every even positive integer m, f(m) represents the product of all even integers from 2 to...

Question

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) ?

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11 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) = 24681012141618202224 =2^12(123456789101112) =2^1212! We break down 12! into prime powers to find its highest prime factor. 12! = 2^103^55^2711 The greatest prime factor is 11

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

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