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What is the greatest prime factor of 2^100 - 2^96?

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IgnitedMind
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What is the greatest prime factor of 2^100 - 2^96? [#permalink] New post   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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C
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Bunuel
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What is the greatest prime factor of 2^100 - 2^96? [#permalink] New post   21 Jan 2013, 10:47
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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.
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x2suresh
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Re: PS Greatest Prime Factors [#permalink] New post   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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ssandeepan
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Re: PS Greatest Prime Factors [#permalink] New post   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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ebliss
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Re: What is the greatest prime factor of 2^100 - 2^96? A. 2 B. [#permalink] New post   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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chiccufrazer1
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Re: What is the greatest prime factor of 2^100 - 2^96? A. 2 B. [#permalink] New post   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 :)

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Re: What is the greatest prime factor of 2^100 - 2^96? A. 2 B. [#permalink] New post   21 Jan 2013, 11:40
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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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What is the greatest prime factor of 2^100 - 2^96? [#permalink] New post   13 Feb 2024, 16:08
­Hi
Can we use the concept of cyclicity in this? 

2^100 will have units digit as 4
and so will 2^96
Subtracting, 4-4 = 0
So 0 is the units place of the difference 
Thus, out ouf all the options, 5 fits the best 

Please let me know­
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What is the greatest prime factor of 2^100 - 2^96? [#permalink]
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