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What is the greatest prime factor of 299 – 296?

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Retired Moderator
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GRE 1: Q167 V156
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What is the greatest prime factor of 299 – 296? [#permalink] New post 25 Aug 2018, 15:11
Expert's post
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Question Stats:

96% (00:21) correct 3% (00:00) wrong based on 28 sessions
What is the greatest prime factor of \(2^{99} – 2^{96}\)?

[Reveal] Spoiler: OA
7

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Sandy
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Re: What is the greatest prime factor of 299 – 296? [#permalink] New post 04 Sep 2018, 11:20
Expert's post
sandy wrote:
What is the greatest prime factor of \(2^{99} – 2^{96}\)?

[Reveal] Spoiler: OA
7


Let's first factor out the 2^96 to get:

2^99 - 2^96 = 2^96(2^3 - 1)
= 2^96(8 - 1)
= 2^96(7)

So, the only prime factors are 2 and 7
The greatest prime factor is 7

Answer: 7

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Brent
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Re: What is the greatest prime factor of 299 – 296? [#permalink] New post 04 Sep 2018, 18:45
The answer is 7.

2^96(2^3-1)= 2^96*7

2^96 consists only of 2's. 7 is a prime number greater than 2
Re: What is the greatest prime factor of 299 – 296?   [#permalink] 04 Sep 2018, 18:45
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What is the greatest prime factor of 299 – 296?

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