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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, 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: 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 :)

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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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Re: PS Greatest Prime Factors [#permalink] New post 11 Sep 2008, 14:28
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, 14:33
x2suresh wrote:
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


same approach, same answer as of suresh....C
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Re: PS Greatest Prime Factors [#permalink] New post 11 Sep 2008, 17:25
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, 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] New post 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] New post 04 Aug 2011, 06:51
C as well. Factor out 2^96
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Re: PS Greatest Prime Factors [#permalink] New post 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] 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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Re: What is the greatest prime factor of 2^100 - 2^96? A. 2 B. [#permalink] New post 21 Jan 2013, 10:47
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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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

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. NEW!!!

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. NEW!!!


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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] 21 Jan 2013, 11:33
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