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oss198
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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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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I just factored all numbers

after doing this over and over again it just takes you around 20 secs.
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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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oss198
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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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.
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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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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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oss198
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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