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Greatest Prime Factor

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Greatest Prime Factor

by money9111 » Tue Feb 09, 2010 1:44 am
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

How do you set this up? Do you just begin by multiplying all even numbers through to 24?
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by harsh.champ » Tue Feb 09, 2010 1:48 am
money9111 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

How do you set this up? Do you just begin by multiplying all even numbers through to 24?
No,that would be a long procedure.
First of all,keep the prime numbers in your mind-2,3,5,7,11,13,17.
Now,since all the no.s are even so 2 is definitely a factor.
Hence,divide all the no.s by 2 ,you get 1,2,3,.....,11,12.
Hence ,you see that 11 is the greatest prime factor. E

This ques. can be solved in 10-15 seconds.Just keep the solution procedure in the mind.:)
Hope you get the approach.:D
Last edited by harsh.champ on Tue Feb 09, 2010 1:51 am, edited 1 time in total.
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by thephoenix » Tue Feb 09, 2010 1:51 am
money9111 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

How do you set this up? Do you just begin by multiplying all even numbers through to 24?
IMO its A

its nothing 24! and greatest prime factor is 23 bcoz its the highest prime no. which 24! has

OA pls
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by harsh.champ » Tue Feb 09, 2010 1:53 am
thephoenix wrote:
money9111 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

How do you set this up? Do you just begin by multiplying all even numbers through to 24?
IMO its A

its nothing 24! and greatest prime factor is 23 bcoz its the highest prime no. which 24! has

OA pls
Hey phoenix,you fell in the trap.[option A was a trap option choice]
Look carefully,it is the product of even no.s
Also look at my soln. above.
I hope you get the mistake.
These types of traps can hamper your score for no reason[as you knew tha approach,just made a silly mistake]
I also make a lot of mistakes like this:-not reading the ques. properly,skipping an imp. part etc.
Hope we can rectify them through practice.:P
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by thephoenix » Tue Feb 09, 2010 1:57 am
harsh.champ wrote:
thephoenix wrote:
money9111 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

How do you set this up? Do you just begin by multiplying all even numbers through to 24?
IMO its A

its nothing 24! and greatest prime factor is 23 bcoz its the highest prime no. which 24! has

OA pls
Hey phoenix,you fell in the trap.[option A was a trap option choice]
Look carefully,it is the product of even no.s
Also look at my soln. above.
I hope you get the mistake.
These types of traps can hamper your score for no reason[as you knew tha approach,just made a silly mistake]
I also make a lot of mistakes like this:-not reading the ques. properly,skipping an imp. part etc.
Hope we can rectify them through practice.:P
yeah thinks...u r correct
its called speed reading syndrome
i will keep that in my mind
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by shashank.ism » Tue Feb 09, 2010 2:18 am
money9111 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

How do you set this up? Do you just begin by multiplying all even numbers through to 24?
f(24)= 24.22...............
just start dividing teh numbers by 2 as all are even.. the first no. which is only divisible by 2 and nothing else than 1, will be the greatest prime number ..
It's simple you don't have to multiply the even numbers..just start diving in mind and u r there..:)
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by shashank.ism » Tue Feb 09, 2010 2:22 am
harsh.champ wrote:
money9111 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

How do you set this up? Do you just begin by multiplying all even numbers through to 24?
No,that would be a long procedure.
First of all,keep the prime numbers in your mind-2,3,5,7,11,13,17.
Now,since all the no.s are even so 2 is definitely a factor.
Hence,divide all the no.s by 2 ,you get 1,2,3,.....,11,12.
Hence ,you see that 11 is the greatest prime factor. E

This ques. can be solved in 10-15 seconds.Just keep the solution procedure in the mind.:)
Hope you get the approach.:D

Well ur very correct in ur approach . But I don't think u have to divide all the numbers in a row. Just start from opposite side. u can solve it much faster
24/2=12 no
22/2 =11 yes..
The game is over..2 sec.
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