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# For every even positive integer m, f(m) represents

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Manager
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For every even positive integer m, f(m) represents  [#permalink]

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07 Jan 2014, 14:51
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80% (01:27) correct 20% (01:30) wrong based on 359 sessions

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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)=2x4x6x8x10x12. What is the greatest prime factor of f(24)?

A. 23
B. 19
C. 17
D. 13
E. 11
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Re: For every even positive integer m, f(m) represents  [#permalink]

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07 Jan 2014, 19:33
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oss198 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)=2x4x6x8x10x12. What is the greatest prime factor of f(24)?

A. 23
B. 19
C. 17
D. 13
E. 11

First let's find out what f(24) is.

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

The prime factors of 24 are 2 and 3.
The prime factors of 22 are 2 and 11.
11 must be the greatest prime factor you will have in this product. Every term smaller than 22 will certainly have 2 as a factor since they are all even so they cannot have another factor greater than 11.

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

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08 Jan 2014, 04:11
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oss198 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)=2x4x6x8x10x12. What is the greatest prime factor of f(24)?

A. 23
B. 19
C. 17
D. 13
E. 11

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Hope this helps.
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Re: For every even positive integer m, f(m) represents  [#permalink]

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08 Jan 2014, 04:39
oss198 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)=2x4x6x8x10x12. 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
now we need greatest prime factor, so we have to check from right to reach the solution faster
prime factors of 24=2,3
prime factors of 22= 2,11
hence 11 will be the greatest prime factor of f(24)
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Re: For every even positive integer m, f(m) represents  [#permalink]

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22 Mar 2017, 14:37
E, because as we know that the set is made of even integers, we can divide 24 by 2
hence 12, 11 is the closest prime
Manager
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Posts: 115
Re: For every even positive integer m, f(m) represents  [#permalink]

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13 May 2017, 06:42
I just factored all numbers

after doing this over and over again it just takes you around 20 secs.
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Re: For every even positive integer m, f(m) represents  [#permalink]

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29 Aug 2017, 07:59
F(24)=2×4×6×8×10×12×14×16×18×20×22×24
The prime factors are 2, 3, 5,7,11 so the LCM is 11.

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

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01 Sep 2017, 11:01
oss198 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)=2x4x6x8x10x12. 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 numbers from 2 to 24 inclusive that 22 (which is 2 x 11) produces the largest prime factor of 11.

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For every even positive integer m, f(m) represents  [#permalink]

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Updated on: 03 Sep 2017, 10:06
The function given is f(24) = 2*4*6*...*24.

f(24) = (2*1) * (2*2) * (2*4) * ... * (2*12). Note that you can further factor out the 2's. There are twelve 2's.

f(24) = (2^12) * (1*2*3*4* ... * 12)

(1*2*3*4* ... * 12) are all factors of f(24) with 11 being the greatest prime factor. Answer is E.

Originally posted by thang62590 on 02 Sep 2017, 07:18.
Last edited by thang62590 on 03 Sep 2017, 10:06, edited 1 time in total.
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Re: For every even positive integer m, f(m) represents  [#permalink]

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02 Sep 2017, 22:25
F(m) =2*4*6......24
=2^12*1*2*3*.....12
=2^12*12!
so we have 11 as the highest prime factor
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Re: For every even positive integer m, f(m) represents  [#permalink]

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22 Oct 2018, 19:36
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Re: For every even positive integer m, f(m) represents   [#permalink] 22 Oct 2018, 19:36
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