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

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What is the greatest prime factor of 2^100 - 2^96? [#permalink] New post 11 Sep 2008, 13:11
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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
[Reveal] Spoiler: OA
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Re: PS Greatest Prime Factors [#permalink] New post 11 Sep 2008, 13:28
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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] New post 11 Sep 2008, 16:25
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] New post 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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Re: PS Greatest Prime Factors [#permalink] New post 11 Sep 2008, 18:14
C

Same explanation as others :
2^96(2^4 -1) = 2^96 * 3*5
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Re: PS Greatest Prime Factors [#permalink] New post 04 Aug 2011, 05:51
C as well. Factor out 2^96
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Re: PS Greatest Prime Factors [#permalink] New post 04 Aug 2011, 13:05
=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] New post 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!
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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, 09:47
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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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Re: What is the greatest prime factor of 2^100 - 2^96? A. 2 B. [#permalink] New post 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.

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, 10:40
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Expert's post
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 :)

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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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: What is the greatest prime factor of 2^100 - 2^96? [#permalink] New post 06 Apr 2014, 06:26
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Re: What is the greatest prime factor of 2^100 - 2^96?   [#permalink] 06 Apr 2014, 06:26
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