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

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Manager
Joined: 28 Aug 2008
Posts: 92
What is the greatest prime factor of 2^100 - 2^96?  [#permalink]

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11 Sep 2008, 13:11
3
11
00:00

Difficulty:

15% (low)

Question Stats:

73% (00:46) correct 27% (01:01) wrong based on 645 sessions

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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
SVP
Joined: 07 Nov 2007
Posts: 1651
Location: New York
Re: PS Greatest Prime Factors  [#permalink]

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11 Sep 2008, 13:28
1
2
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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Manager
Joined: 09 Jul 2007
Posts: 210
Re: PS Greatest Prime Factors  [#permalink]

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11 Sep 2008, 16:25
1
2^100 - 2^96=2^96 ( 2^4-1)=2^96*3*5

so greatest prime factor =5
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Joined: 17 Jun 2008
Posts: 1200
Re: PS Greatest Prime Factors  [#permalink]

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11 Sep 2008, 18:10
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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Joined: 21 Apr 2008
Posts: 260
Location: Motortown
Re: PS Greatest Prime Factors  [#permalink]

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11 Sep 2008, 18:14
C

Same explanation as others :
2^96(2^4 -1) = 2^96 * 3*5
Senior Manager
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Posts: 354
Location: United States (WI)
GMAT 1: 780 Q49 V50
WE: Research (Other)
Re: PS Greatest Prime Factors  [#permalink]

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04 Aug 2011, 05:51
C as well. Factor out 2^96
Director
Joined: 01 Feb 2011
Posts: 654
Re: PS Greatest Prime Factors  [#permalink]

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04 Aug 2011, 13:05
=2^96(15) = 2^96*3*5

Greatest prime factor = 5.

Intern
Joined: 14 Jul 2012
Posts: 1
Re: What is the greatest prime factor of 2^100 - 2^96? A. 2 B.  [#permalink]

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21 Jan 2013, 09:20
Can someone please explain how we can go from 2^4 * 2^96 - 2^96 to 2^96 (16-1) ?

Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 52917
Re: What is the greatest prime factor of 2^100 - 2^96? A. 2 B.  [#permalink]

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21 Jan 2013, 09:47
3
1
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.

Hope it's clear.
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Joined: 04 Jan 2013
Posts: 69
Re: What is the greatest prime factor of 2^100 - 2^96? A. 2 B.  [#permalink]

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21 Jan 2013, 10:33
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.

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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Math Expert
Joined: 02 Sep 2009
Posts: 52917
Re: What is the greatest prime factor of 2^100 - 2^96? A. 2 B.  [#permalink]

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21 Jan 2013, 10:40
1
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.

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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14 Mar 2016, 01:16
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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Posts: 92
Re: What is the greatest prime factor of 2^100 - 2^96?  [#permalink]

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14 Mar 2016, 04:05
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.
Current Student
Joined: 12 Aug 2015
Posts: 2621
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: What is the greatest prime factor of 2^100 - 2^96?  [#permalink]

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16 Mar 2016, 01:37
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, 01:44
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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23 Oct 2018, 07:02
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Re: What is the greatest prime factor of 2^100 - 2^96?   [#permalink] 23 Oct 2018, 07:02
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