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What is the greatest prime factor of 6^8−3^8 ?
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15 Feb 2016, 13:48
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63% (01:39) correct 37% (01:38) wrong based on 502 sessions
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What is the greatest prime factor of \(6^8−3^8\) ? A) 3 B) 11 C) 17 D) 19 E) 31
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Re: What is the greatest prime factor of 6^8−3^8 ?
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15 Feb 2016, 13:55
Quote: What is the greatest prime factor of 6⁸ − 3⁸? a) 3 b) 11 c) 17 d) 19 e) 31 Thanks in advance 6⁸ − 3⁸ is a DIFFERENCE OF SQUARES. So we can factor it. 6⁸ − 3⁸ = (6⁴ + 3⁴)(6⁴  3⁴) = (6⁴ + 3⁴)(6² + 3²)(6²  3²) = (6⁴ + 3⁴)(6² + 3²)(6 + 3)(6  3) = (6⁴ + 3⁴)(45)(9)(3) = ( 6⁴ + 3⁴)(3)(3)(5)(3)(3)(3) Hmmmm, we can see that the correct answer is "hiding" in the first number ( 6⁴ + 3⁴) Let's factor out the 3⁴, to get: 6⁴ + 3⁴ = 3⁴(2⁴ + 1) = 3⁴(16 + 1) = 3⁴(17) = (3)(3)(3)(3)(17)So, 6⁸ − 3⁸ = (3)(3)(3)(3)(17)(3)(3)(5)(3)(3)(3) So the correct answer is C ASIDE: For more on factoring differences of squares, see our free video  http://www.gmatprepnow.com/module/gmat ... /video/955Cheers, Brent
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What is the greatest prime factor of 6^8−3^8 ?
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Updated on: 15 Feb 2016, 14:03
\(6^8  3^8\)
\(2^8*3^8  3^8\)
\(3^8(2^8  1)\)
\((2^4 + 1)(2^4  1)\)
\((16+1)(161)\)
\((17)(15)\)
So 17 is Answer
Originally posted by zxcvbnmas on 15 Feb 2016, 13:56.
Last edited by zxcvbnmas on 15 Feb 2016, 14:03, edited 1 time in total.




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Re: What is the greatest prime factor of 6^8−3^8 ?
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15 Feb 2016, 14:01
zxcvbnmas wrote: What is the greatest prime factor of \(6^8−3^8\) ?
A) 3
B) 11
C) 17
D) 19
E) 31 Solution: \(6^83^8=3^8*(2^81)=3^8(2561)=3^8(255)=3^8*51*5=3^8*17*3*5\). ANS .17



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Re: What is the greatest prime factor of 6^8−3^8 ?
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09 Jul 2016, 13:05
how do u solve this? how do u know what methodology to apply when u get a question like this? im soo confused!!



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What is the greatest prime factor of 6^8−3^8 ?
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09 Jul 2016, 23:27
jonmarrow wrote: how do u solve this? how do u know what methodology to apply when u get a question like this? im soo confused!! To find the greatest prime of 6^8−3^8 you should make prime factorization of this number. The techniques above does exactly this. Check similar questions to practice: whatisthegreatestprimefactorof158991.htmlwhatisthegreatestprimefactorof104757.htmlwhatisthegreatestprimefactorof70126.htmlwhatisthegreatestprimefactorof190425.htmlHope it helps.
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What is the greatest prime factor of 6^8−3^8 ?
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Updated on: 06 Apr 2018, 00:20
First figure out the common factors in both \(6^8\) can be written s \(2^8 * 3^8\) \(take 3^8 common\) \(3^8*2^83^8\) \(3^8(2^81)\) (here you should know that \(2^8 = 256\), The easiest way to remember this is \(2^{10}=1024\) and now you can derive most \(2^x\)) SO your expression becomes \(3^8(2561)\) ===> \(3^8 (255)\)==>\(3^8 (17*15)\) so your prime factorisation will be \(3^8*15*17\)===>\(3^8*(3^1*5^1)*17\)=====>\(3^9*5^1*17\) so as we can see there are there prime numbers here 3, 5 and 17 out of which 3 is the smallest prime number and 17 is the biggest. Hence 17 is the biggest Prime Factor Answer is C zxcvbnmas wrote: What is the greatest prime factor of \(6^8−3^8\) ?
A) 3
B) 11
C) 17
D) 19
E) 31
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Originally posted by LogicGuru1 on 10 Jul 2016, 01:40.
Last edited by LogicGuru1 on 06 Apr 2018, 00:20, edited 1 time in total.



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Re: What is the greatest prime factor of 6^8−3^8 ?
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11 Jul 2016, 05:06
3^8(2^81)=3^8(255) =3^8(17*15)=3^8*17*5*3=3^9*5*17 therefore 17 C



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Re: What is the greatest prime factor of 6^8−3^8 ?
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14 Jul 2016, 20:57
AdlaT wrote: zxcvbnmas wrote: What is the greatest prime factor of \(6^8−3^8\) ?
A) 3
B) 11
C) 17
D) 19
E) 31 Solution: \(6^83^8=3^8*(2^81)=3^8(2561)=3^8(255)=3^8*51*5=3^8*17*3*5\). ANS .17 what about 3^8, it could have a prime factor greater than 17.



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Re: What is the greatest prime factor of 6^8−3^8 ?
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14 Jul 2016, 21:08
ramanan42 wrote: AdlaT wrote: zxcvbnmas wrote: What is the greatest prime factor of \(6^8−3^8\) ?
A) 3
B) 11
C) 17
D) 19
E) 31 Solution: \(6^83^8=3^8*(2^81)=3^8(2561)=3^8(255)=3^8*51*5=3^8*17*3*5\). ANS .17 what about 3^8, it could have a prime factor greater than 17. understood the reasoning behind this . ! good now!



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Re: What is the greatest prime factor of 6^8−3^8 ?
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10 Apr 2017, 18:49
GMATPrepNow wrote: Quote: What is the greatest prime factor of 6⁸ − 3⁸? a) 3 b) 11 c) 17 d) 19 e) 31 Thanks in advance 6⁸ − 3⁸ is a DIFFERENCE OF SQUARES. So we can factor it. 6⁸ − 3⁸ = (6⁴ + 3⁴)(6⁴  3⁴) = (6⁴ + 3⁴)(6² + 3²)(6²  3²) = (6⁴ + 3⁴)(6² + 3²)(6 + 3)(6  3) = (6⁴ + 3⁴)(45)(9)(3) = ( 6⁴ + 3⁴)(3)(3)(5)(3)(3)(3) Hmmmm, we can see that the correct answer is "hiding" in the first number ( 6⁴ + 3⁴) Let's factor out the 3⁴, to get: 6⁴ + 3⁴ = 3⁴(2⁴ + 1) = 3⁴(16 + 1) = 3⁴(17) = (3)(3)(3)(3)(17)So, 6⁸ − 3⁸ = (3)(3)(3)(3)(17)(3)(3)(5)(3)(3)(3) So the correct answer is C ASIDE: For more on factoring differences of squares, see our free video  http://www.gmatprepnow.com/module/gmat ... /video/955Cheers, Brent It's interesting to see all the different methodologies here many paths that lead to the same answers; anyways, my method following this technique was slightly different. When you mention the answer lies in (6^4 + 3^4) 3^4(3^4 +1) 81 (82) 82/2 = 41/3 = 17 (plug in values)



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Re: What is the greatest prime factor of 6^8−3^8 ?
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08 Jul 2017, 14:59
zxcvbnmas wrote: What is the greatest prime factor of \(6^8−3^8\) ?
A) 3
B) 11
C) 17
D) 19
E) 31 In order to find the greatest prime factor, lets break down the below number into its prime factors \(6^8−3^8\) = \((3^8 * 2^8) − 3^8\) = \((3^8 * 2^8) − 3^8\) = \(3^8 (2^8  1)\) = \(3^8 * 255\) = \(3^8 * 15 * 17\) = \(3^9 * 5 * 17\) As we can see that the greatest prime factor is \(17\) Answer is C
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Re: What is the greatest prime factor of 6^8−3^8 ?
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08 Feb 2018, 12:38
Hi All, If you're comfortable with Exponent Rules and Factoring, you can also approach this prompt without using a Quadratic: 6^8  3^8 = First, we can 'rewrite' 6^8.... (2^8)(3^8)  3^8 Now, factor out 3^8... (3^8)(2^8  1) 2^8 = 256 (3^8)(2561) (3^8)(255) (3^8)(5)(51) (3^8)(5)(3)(17) The greatest prime factor is 17. Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: What is the greatest prime factor of 6^8−3^8 ?
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05 Aug 2018, 09:21
6^83^8= 3^8*2^83^8= 3^8(2^81)= 3^8(2561)= 3^8(255)= 3^8(3*5*17) Answ is 17 (C)
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Re: What is the greatest prime factor of 6^8−3^8 ?
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05 Aug 2018, 10:54
zxcvbnmas wrote: What is the greatest prime factor of \(6^8−3^8\) ?
A) 3
B) 11
C) 17
D) 19
E) 31 \(6^8−3^8\) = \(2^8*3^8−3^8\) = \(3^8(2^8 −1)\) Now, \(2^8 − 1\) \(= 255 = 15*17\), So The greatest Prime number is 17 Answer must be (C)
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Re: What is the greatest prime factor of 6^8−3^8 ?
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20 May 2019, 15:11
It should be 17, since we can use a^2  b^2 here. C



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Re: What is the greatest prime factor of 6^8−3^8 ?
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20 May 2019, 16:46
zxcvbnmas wrote: What is the greatest prime factor of \(6^8−3^8\) ?
A) 3
B) 11
C) 17
D) 19
E) 31 Prime factor is a number that is divisible by only one and itself; e.g. 3, 5, 19 etc. We have to break down this number as far as possible. 3^8 * (2^8  1) 3^8 * (255) 3^8 * (51*5) 3^8 * (5)(17*3) So, this number can be factorized into following primes: 3, 5, 17. 17 being the greatest.
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Re: What is the greatest prime factor of 6^8−3^8 ?
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