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What is the greatest prime factor of 2^100 - 2^96? [#permalink]
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 11 Sep 2008, 14:11
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What is the greatest prime factor of 2^100 - 2^96? A. 2 B. 3 C. 5 D. 7 E. 11
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Re: PS Greatest Prime Factors [#permalink]
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11 Sep 2008, 14:28
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IgnitedMind wrote: What is the greatest prime factor of 2^100 - 2^96?
A. 2
B. 3
C. 5
D. 7
E. 11 2^100 - 2^96 = 2^4*2^96 -2^96 = 2^96 (16-1) = 2^96 *5*3 5 is the greatest factor C
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Re: PS Greatest Prime Factors [#permalink]
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11 Sep 2008, 17:25
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2^100 - 2^96=2^96 ( 2^4-1)=2^96*3*5
so greatest prime factor =5
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Re: PS Greatest Prime Factors [#permalink]
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11 Sep 2008, 19:10
IgnitedMind wrote: What is the greatest prime factor of 2^100 - 2^96?
A. 2
B. 3
C. 5
D. 7
E. 11 IMO C 2^96(16-1)=2^96 * 3*5 => 5 is the greatest prime factor
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Re: PS Greatest Prime Factors [#permalink]
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11 Sep 2008, 19:14
C
Same explanation as others :
2^96(2^4 -1) = 2^96 * 3*5
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Re: PS Greatest Prime Factors [#permalink]
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04 Aug 2011, 06:51
C as well. Factor out 2^96
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Re: PS Greatest Prime Factors [#permalink]
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04 Aug 2011, 14:05
=2^96(15) = 2^96*3*5
Greatest prime factor = 5.
Answer is C.
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Re: What is the greatest prime factor of 2^100 - 2^96? A. 2 B. [#permalink]
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21 Jan 2013, 10:20
Can someone please explain how we can go from 2^4 * 2^96 - 2^96 to 2^96 (16-1) ?
Thanks!
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Re: What is the greatest prime factor of 2^100 - 2^96? A. 2 B. [#permalink]
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21 Jan 2013, 10:47
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Re: What is the greatest prime factor of 2^100 - 2^96? A. 2 B. [#permalink]
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21 Jan 2013, 11:33
Bunuel wrote: ebliss wrote: Can someone please explain how we can go from 2^4 * 2^96 - 2^96 to 2^96 (16-1) ?
Thanks! Sure. What is the greatest prime factor of 2^100 - 2^96?A. 2 B. 3 C. 5 D. 7 E. 11 \(2^{100} - 2^{96}=2^4*2^{96}-2^{96}\). Now, factor out 2^{96}: \(2^4*2^{96}-2^{96}=2^{96}(2^4-1)=2^{96}*15=2^{96}*3*5\). The greatest prime factor is 5. Answer: C. Hope it's clear. @bunuel..2^96-2^96=2^1 according to index laws..in our factorised equation 2^4*2^96-2^96 the answer is 16*2=32..can we do prime factorisation on 32 where by k/2 +k/3 +k/5--->32/2+32/3+32/5?would we just take the 5 as our largest factor?but we know 5 is not a factor of 32..where am i missing the details please tell me..thanks in advance  Posted from my mobile device
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Re: What is the greatest prime factor of 2^100 - 2^96? A. 2 B. [#permalink]
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21 Jan 2013, 11:40
chiccufrazer1 wrote: Bunuel wrote: ebliss wrote: Can someone please explain how we can go from 2^4 * 2^96 - 2^96 to 2^96 (16-1) ?
Thanks! Sure. What is the greatest prime factor of 2^100 - 2^96?A. 2 B. 3 C. 5 D. 7 E. 11 \(2^{100} - 2^{96}=2^4*2^{96}-2^{96}\). Now, factor out 2^{96}: \(2^4*2^{96}-2^{96}=2^{96}(2^4-1)=2^{96}*15=2^{96}*3*5\). The greatest prime factor is 5. Answer: C. Hope it's clear. @bunuel..2^96-2^96=2^1 according to index laws..in our factorised equation 2^4*2^96-2^96 the answer is 16*2=32..can we do prime factorisation on 32 where by k/2 +k/3 +k/5--->32/2+32/3+32/5?would we just take the 5 as our largest factor?but we know 5 is not a factor of 32..where am i missing the details please tell me..thanks in advance Posted from my mobile device Not sure I understand your post. First of all, 2^96-2^96=0 not 2. Next, \(2^4*2^{96}-2^{96}\) equals to \(2^{96}*3*5\) not 32.
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Re: What is the greatest prime factor of 2^100 - 2^96? [#permalink]
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Re: What is the greatest prime factor of 2^100 - 2^96? [#permalink]
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Re: What is the greatest prime factor of 2^100 - 2^96? [#permalink]
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14 Mar 2016, 02:16
here taking 2^96 out as a common factor we are left with 15=5 x 3 hence 5 is the highest common factor
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Re: What is the greatest prime factor of 2^100 - 2^96? [#permalink]
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14 Mar 2016, 05:05
IgnitedMind wrote: What is the greatest prime factor of 2^100 - 2^96?
A. 2
B. 3
C. 5
D. 7
E. 11 It can be written as 2^96(2^4-1), which has prime factors as 2, 3, and 5.
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Re: What is the greatest prime factor of 2^100 - 2^96? [#permalink]
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16 Mar 2016, 02:37
here again we factor out 2^96 and we get => 15 so 5 is the highest prime hence C
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Re: What is the greatest prime factor of 2^100 - 2^96? [#permalink]
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16 Mar 2016, 02:44
IgnitedMind wrote: What is the greatest prime factor of 2^100 - 2^96?
A. 2
B. 3
C. 5
D. 7
E. 11 The given expression can be written as 2^96(2^4 -1) = 2^96 * 3*5
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Re: What is the greatest prime factor of 2^100 - 2^96? [#permalink]
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27 May 2017, 11:58
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Re: What is the greatest prime factor of 2^100 - 2^96?
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27 May 2017, 11:58
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