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

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oss198
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For every even positive integer m, f(m) represents [#permalink] New post  07 Jan 2014, 15:51
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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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KarishmaB
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Re: For every even positive integer m, f(m) represents [#permalink] New post  07 Jan 2014, 20:33
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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.

Answer (E)
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Bunuel
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Re: For every even positive integer m, f(m) represents [#permalink] New post  08 Jan 2014, 05:11
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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


Similar questions to practice:
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for-every-positive-even-integer-n-the-function-h-n-149722.html
for-any-integer-p-p-is-equal-to-the-product-of-all-the-int-112494.html
x-is-the-product-of-all-even-numbers-from-2-to-50-inclusive-156545.html
if-a-and-b-are-odd-integers-a-b-represents-the-product-of-144714.html

Hope this helps.
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bharatdivvela
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Re: For every even positive integer m, f(m) represents [#permalink] New post  08 Jan 2014, 05:39
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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



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] New post  22 Mar 2017, 15:37
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
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daviddaviddavid
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Re: For every even positive integer m, f(m) represents [#permalink] New post  13 May 2017, 07:42
I just factored all numbers

after doing this over and over again it just takes you around 20 secs.
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pinkAugust2308
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Re: For every even positive integer m, f(m) represents [#permalink] New post  29 Aug 2017, 08:59
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.
Answer is E.

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Re: For every even positive integer m, f(m) represents [#permalink] New post  01 Sep 2017, 12:01
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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


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.

Answer: E
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For every even positive integer m, f(m) represents [#permalink] New post  Updated on: 03 Sep 2017, 11:06
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, 08:18.
Last edited by thang62590 on 03 Sep 2017, 11:06, edited 1 time in total.
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Re: For every even positive integer m, f(m) represents [#permalink] New post  02 Sep 2017, 23:25
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] New post  14 Sep 2023, 10:08
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)?

f(24) = 24x22x20x18x......2
24= 2x2x2x3
22=2x11
18=2x9

As we until 2, we will get the no.s in the form of 2k where k is an integer, since 22 is the no. when broken down yields 2x11 where 11 is the maximum value of prime no., 11 is the answer

Hence E
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Abhishek009
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Re: For every even positive integer m, f(m) represents [#permalink] New post  14 Sep 2023, 11:12
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

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

Here, \(22 = 2*11\), thus Answer must be (E) 11
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