What is the greatest prime factor of 2^100 - 2^96? : Problem Solving (PS)

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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]

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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

Spoiler: OA

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Re: PS Greatest Prime Factors [#permalink]

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11 Sep 2008, 13:28

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]

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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]

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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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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

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Re: PS Greatest Prime Factors [#permalink]

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04 Aug 2011, 05:51

C as well. Factor out 2^96

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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.

Answer is C.

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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, 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]

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21 Jan 2013, 09:47

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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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!

@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]

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21 Jan 2013, 10:40

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!

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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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.

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Re: What is the greatest prime factor of 2^100 - 2^96? [#permalink]

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16 Mar 2016, 01:37

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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