For every even positive integer m, f(m) represents the product of all

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

(A) 23
(B) 19
(C) 17
(D) 13
(E) 11

Bunuel · Accepted Answer

SOLUTION

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

(A) 23
(B) 19
(C) 17
(D) 13
(E) 11

\(f(24) = 2*4*6*8*10*12*14*16*18*20*22*24 =\)
\(=2^{12}*(1*2*3*4*5*6*7*8*9*10*11*12)\).

The greatest prime factor is 11.

Answer: E.

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PareshGmat · Answer

Answer = (E) 11

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

22 = 2 * 11

So 11 is the largest prime factor, Answer = E

WoundedTiger · Answer

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

(A) 23
(B) 19
(C) 17
(D) 13
(E) 11

Sol: f(24)= 2*4*6**....*24
or 2^12 (1*2*3*4*5*6....12)

The greatest prime factor will be 11

Ans is E

CCMBA · Answer

All numbers are even. The only even prime is 2. For larger primes, we need a number with an odd factor. Consider 6, 10,...,22. The prime factorization of 22 is 2*11. The answer is E.

unceldolan · Answer

We have 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

Now the greatest prime factor of the product will be the greatest prime factor of one of the numbers above.

22 = 2 x 11 Hence greatest prime factor = 11.

Ans. E

reza52520 · Answer

Very easy,..think simply. The highest number can be divided by a highest prime is 22/11. so 11 is the answer GIve Kudos if you like my solution :lol:

Ndkms · Answer

Best answer hands down.

By the way ... does anybody know what should be the take away message from this question?

JeffTargetTestPrep · Answer

We are given that for every even positive integer m, f(m) represents the product of all even integers from 2 to m inclusive.

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

Shiv2016 · Answer

Check out the options:
Whatever the answer is, it should be a multiple of 2. (2* prime no.)

(1) 23*2= 46 (out of range)
(2) 19*2= 38 (out of range)
(3) 17*2= 34 (out of range)
(4) 13*2= 26 (out of range)
(5) 11*2= 22 (Correct answer)

matthewsmith_89 · Answer

My approach:

f(24) = 2 x 4 x 6 x 8 x 10 x12 x 14 x 16 x 18 x 20 x 22 x 24
f(24) = 2 x 2² x2 x 3 x 2³ x 2 x 5 x 2² x 3 x 2 x 7 x 2⁴ x 2 x 3² x 2² x 5 x 2 x 11 x 2³ x 3

Answer is E. 11

JeffTargetTestPrep · Answer

We are given that for every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. We need to determine the greatest prime factor of f(24).

f(24) = 2 x 4 x 6 x … x 20 x 22 x 24

We see from the even multiples from 2 to 24, that 22 (which is 2 x 11) produces the largest prime factor of 11.

Answer: E

AyushCrackVerbal · Answer

f(24) = 2*4*6*8*10*12*14*16*18*20*22*24

f(24)  = 2^12 *(1*2*3*4*5*6*7*8*9*10*11*12)

The greatest prime factor in f(24) is 11.

The correct answer is  E

Loop123 · Answer

This was Question number 145 from quant review 2019.How come difficulty is "sub-@600"?  Bunuel

Bunuel · Answer

The difficulty level of a question is calculated  automatically  based on the timer stats from the users which attempted the question. Based on 1067 sessions it IS a sub-600 question.

Loop123 · Answer

I used to think it was getting harder in official reviews as the question number goes up. Bunuel thanks for the reply,first time tried it

Alextaller81 · Answer

I dont get it can someone explain and break it down?

kokus · Answer

The question tells us that f is the product of all even integers from 2 to 24. Can we built a prime which is a factor of any of the numbers in this sequence and is also an answer choice?

24? 2^2*3 -> No such answer
22? 2*11 -> Bingo

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For every even positive integer m, f(m) represents the product of all

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