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

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

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

KarishmaB · Accepted Answer

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)

Bunuel · Answer

Similar questions to practice: for-every-positive-even-integer-n-the-function-h-n-is-126691.html 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.

bharatdivvela · Answer

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)

SeregaP · Answer

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

daviddaviddavid · Answer

I just factored all numbers

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

pinkAugust2308 · Answer

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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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 numbers from 2 to 24 inclusive that 22 (which is 2 x 11) produces the largest prime factor of 11.

Answer: E

thang62590 · Answer

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.

arvind910619 · Answer

F(m) =2*4*6......24
=2^12*1*2*3*.....12
=2^12*12!
so we have 11 as the highest prime factor

Paras96 · 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)=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

Abhishek009 · Answer

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

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

bumpbot · Answer

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

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

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