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Manager
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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 08:45
Well first we have to find F(12)= 2^2*3
The greatest prime factor of f(12) is 3, now g(3)= 2^3 + 1=9
9=3*3
So smallest prime factor is 3
thus g(f(12))= 3



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 08:46
IMO B
For every positive integer x, f(x) represents the greatest prime factor of x!, and g(x) represents the smallest prime factor of 2^x+1. What is (g(f(12))?
Given, f(12) represents the greatest prime factor of 12!, which is 11, as we know 12! = 12*11*10*9*8*7*6*5*4*3*2*1
Now g(11) represents the smallest prime factor of 2^11+1 = 2048+1 = 2049, which is 3 (2049=3*683, we do not need to calculate all prime factors as we only need the smallest one which is 3)
So, (g(f(12)) = 3



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For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 08:49
Greatest prime factor of 12! will be 11. So f(12)=11 g(11)=smallest prime factor of 2^11+1=Smallest prime factor of 2049 which is 3 (2+0+4+9=15 which is divisible by 3 as per divisibility rules)
IMO B



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 08:51
IMO correct answer is B  3 explanation as attached
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For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 08:53
1) f(12) is the greatest prime factor of 12!, which is 11 2) g(11) is the smallest prime factor of \(2^{11}+1=2049\). not divisible by 2 (the lowest prime) as 2049 is odd, but divisible by 3 (the secondlowest prime) as 2+0+4+9=15, which is divisible by 3
So g(f(12))=3
IMo Ans: B



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 08:54
IMO B.
f(x) = largest prime factor of x! g(x)= smallest prime factor of \(2^x+1\)
g(f(12)), f(12) > largest prime factor of 12! > 12X11X10X...1 > Highest prime factor would be 11. g(11)= 2^11+1= 2048 + 1 = 2049 . 2049 is not divisible by 2 but is divisble by 3 which is a prime number.
Hence, the answer is 3 which is option B.



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 08:55
For every positive integer x, f(x) represents the greatest prime factor of x!, and g(x) represents the smallest prime factor of 2x+1. What is (g(f(12))?
Lets find inner equation value first i.e f(12) = 12! > What is the greatest prime factor of 12! > 11 g(11) = \(2^{11}\) + 1 = 2048 +1 = 2049 > What is the smallest prime factor of 2049 2049 is not divisible by 2 Find out if no if divisible by 3  add the digits = sum is divisible by 3, hence 2049 is divisible by 3.. smallest prime factor is 3
B is the answer



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 08:57
Quote: For every positive integer x, f(x) represents the greatest prime factor of x!, and g(x) represents the smallest prime factor of 2ˆx+1. What is (g(f(12))?
A. 2 B. 3 C. 5 D. 7 E. 11 f(12) is g8primefac of 12!, which is the largest prime from 0 to 12 = 11; g(11) is smallest prime factor of 2ˆ(11)+1=2048+1=2049, notice that 2049 is not divisible by 2, but the sum of its digits is a multiple of 3, so its divisible by 3, which means the smallest pf is 3. Answer (B).



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 08:58
IMOB
f(x) = Greatest prime factor of x! g(x) = Smallest prime factor of 2^x + 1
f(12)= Greatest prime factor of 12! = Greatest prime factor ( 12 x 11 x 10 x 9..........x1) = 11 g(11)= Smallest prime factor of 2^11 + 1= Smallest prime factor of 2049 = 3
g(f(12))= g(11)= 3



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 08:59
Given that f(x) represents the greatest prime factor of x! And g(x) represents the smallest prime factor of (2^x) + 1 to find g(f(12)) f(12): since 12! has 11 as the greatest prime factor therefore, f(12) = 11 Also for g(f(12)): we have (2^11) + 1 = 2049 2049/3 = 683 thus, 3 is the smallest prime factor of g(f(12)) Final answer is 3 Hence answer choice B.Thank you for kudos.
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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 09:04
(g(f(12)) : F(12)  represent the greatest prime of 12! = 11
g(11) = 2^11+1
The last digit of 2^11 = 4 (based on the pattern of 2,4,8,6) So the smallest prime or the prime that divides g(11) is 5
IMO : C



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 09:05
First we have 12!
It can be written as
2^10*3^5*5^2*7*11
Greatest prime factor is 11
Then we have 2^11+1
2049 ,this is not divisible by 11 or 7 or 5 or 2
This is divisible by 3
B it is !!
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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 09:06
For every positive integer x, f(x) represents the greatest prime factor of x!, and g(x) represents the smallest prime factor of \(2^x+1\). What is (g(f(12))?
Start by finding f(12) f(12) = GREATEST prime factor of 12! 12! = 12x11x10x9x8x7x6x5x4x3x2x1
11 is the greatest prime factor
f(12) = 11
g(f(12)) = g(11)
SMALLEST prime factor of \(2^{11} + 1\) = 2048 + 1 = 2049
2049 is not divisible by 2 2049 is divisible by 3.... so 3 is the smallest prime factor of 2049
g(11) = 3 = g(f(12))
Answer: B  3



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 09:10
f(x) represents the greatest prime factor of x! f(12) => 12! = 12*11*10*9*8*7*6*5*4*3*2*1 Thus greatest prime factor is 11.
g(x) represents the smallest prime factor of \(2^x\)+1 g(11) => \(2^{11}\) + 1 => 2049 2049 = 3*683 Thus smallest prime factor is 3.
IMO the answer is B.
Please hit kudos if you like the solution.



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 09:31
f(12) is highest prime factor of 12! which is 11. so g(11) will be lowest prime factor of (2^11+1) => Plowest ( 2049) => 3
Answer shall be B.
Regards, Rishav



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 09:42
For every positive integer xx, f(x) represents the greatest prime factor of x! and g(x) represents the smallest prime factor of 2^x+1. What is (g(f(12))?
A. 2 B. 3 C. 5 D. 7 E. 11
Solution f(12) = highest prime factor for 12! and that would be 11 g(11) = 2^11 +1 = odd number option A out 2^11+1 = 2^10 * 2+1 1024*2 +1 = 2049, which is divisible by 3 hence g(11) wud be the smallest prime factor i.e. 3
Answer = B



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 09:44
For every positive integer x x , f(x) f(x) represents the greatest prime factor of x! x! , and g(x) g(x) represents the smallest prime factor of 2 x +1 2x+1 . What is (g(f(12)) (g(f(12)) ?
A. 2 B. 3 C. 5 D. 7 E. 11 Solution: Its given that for every positive integer x,f(x) represent the greatest prime factor of x!,this implies that from question f(12)=greatest prime factor of 12! factors of 12!=12*11*10*9*8*7*6*5*4*3*2*1=11*7*\(5^(2)\)*\(3^(5)\)*\(2^(10)\)
As the greatest prime factor is 11 ,hence it implies we need to calculate g(11)=2^(11) +1=2048+1=2049 Now factor of 2049=3*683 Hence g(11)=smallest prime factor of\(2^(11)\) +1=smallest prime factor of 3*683=3 Hence B IMO



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 10:39
We need to find g(f(12))
f(12), the greatest prime of 12! is 11 Now, g(11), smallest prime factor of 2^11 + 1 = 2048+1 = 2049
Smallest prime number by which 2049 is 3 (using divisibility rule for 3)
B is correct.



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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 10:43
f(12) greatest prime factor of 12 will be 3. Therefore question becomes g(3) =2^3+1=9 Smallest prime factor of 9 is 3 so the answer option B
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Re: For every positive integer x, f(x) represents the greatest prime fact
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18 Jul 2019, 11:07
Given,
1. f(x) => Greatest prime factor of x! 2. g(x) => Smallest prime factor of 2^x + 1
To find,
g(f(12))
Lets do it step by step,
Step 1:
f(12) = Greatest prime factor of 12!
12! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12
=> f(12) = 11
Step 2:
g(x) => Smallest prime factor of 2^x + 1
g(f(12)) = g(11) = Smallest prime factor of 2^11 + 1
=> Smallest prime factor of 2048 + 1 = 2049
Let us check the options which divide 2049
A. 2 > Wrong. Is not a factor of 2049.
B. 3 > Correct. Divides 2049 and is the smallest.
C. 5 > Wrong. Is not a factor of 2049.
D. 7 > Wrong. Is not a factor of 2049.
E. 11 > Wrong. Is not a factor of 2049.




Re: For every positive integer x, f(x) represents the greatest prime fact
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