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

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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
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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
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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
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.
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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
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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
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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
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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
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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
Bunuel wrote:
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) --> the greatest prime factor is 11.

By the way ... does anybody know what should be the take away message from this question?
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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

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.

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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
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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)

Originally posted by Shiv2016 on 03 Apr 2017, 07:10.
Last edited by Shiv2016 on 03 Apr 2017, 11:34, edited 2 times in total.
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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
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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

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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
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Bunuel wrote:

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

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.

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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
$$f(24) = 2*4*6*8*10*12*14*16*18*20*22*24$$

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

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

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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
This was Question number 145 from quant review 2019.How come difficulty is "sub-@600"? Bunuel
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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
Muammer wrote:
This was Question number 145 from quant review 2019.How come difficulty is "sub-@600"? Bunuel

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.
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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
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
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Re: For every even positive integer m, f(m) represents the product of all [#permalink]
I dont get it can someone explain and break it down?
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For every even positive integer m, f(m) represents the product of all [#permalink]
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
For every even positive integer m, f(m) represents the product of all [#permalink]
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