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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
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.
_________________
Re: What is the greatest prime factor of 2^100 - 2^96? [#permalink]
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06 Apr 2014, 07:26
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Re: What is the greatest prime factor of 2^100 - 2^96? [#permalink]
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27 Jul 2015, 07:55
Hello from the GMAT Club BumpBot!
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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
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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71% (00:28) correct
