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

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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)?

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.

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)?

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

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08 Jan 2014, 05:39

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)

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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