Official Guide
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 \(f(24)\)?
A. 23
B. 19
C. 17
D. 13
E. 11
OA E
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For every even positive integer m, f(m) represents the
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f(24) = 2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 x 22 x 24AAPL wrote:Official Guide
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 \(f(24)\)?
A. 23
B. 19
C. 17
D. 13
E. 11
OA E
Rewrite as prime factorization: f(24) = 2 x (2)(2) x (2)(3) x (2)(2)(2) x (2)(5) x (2)(2)(3) x (2)(7) x (2)(2)(2)(2) x (2)(3)(3) x (2)(2)(5) x (2)(11) x (2)(2)(2)(3)
Answer: E
ASIDE: As you can see from the answer choice, I really didn't need to find the prime factorization of EVERY value.
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We are given that for every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive.AAPL wrote:Official Guide
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 \(f(24)\)?
A. 23
B. 19
C. 17
D. 13
E. 11
OA E
Thus, f(24) = 2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 x 22 x 24.
If we were to break each value into primes, we would see that the greatest prime factor is contained in 22 (which equals 2 x 11).
Thus, the largest prime factor in f(24) is 11.
Answer: E
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