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If x = 2^7^4 - 2^7^0, what is the largest

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If x = 2^7^4 - 2^7^0, what is the largest [#permalink] New post 29 Aug 2018, 06:53
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If \(x = 2^7^4 - 2^7^0\), what is the largest prime factor of x?

A)2
B)3
C)5
D)7
E)11

src:orbit test prep
[Reveal] Spoiler: OA
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Re: If x = 2^7^4 - 2^7^0, what is the largest [#permalink] New post 29 Aug 2018, 07:19
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amorphous wrote:
If \(x = 2^7^4 - 2^7^0\), what is the largest prime factor of x?

A)2
B)3
C)5
D)7
E)11


Given: x = 2^74 - 2^70
Factor 2^70 from right side to get: x = 2^70(2^4 - 1)
Evaluate to get: x = 2^70(16 - 1)
Simplify to get: x = (2^70)(15)
Factor 15 to get: x = (2^70)(3)(5)

So, there are 3 different prime factors: 2, 3 and 5
The greatest prime is 5

Answer: C

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: If x = 2^7^4 - 2^7^0, what is the largest [#permalink] New post 07 Sep 2018, 19:44
amorphous wrote:
If \(x = 2^7^4 - 2^7^0\), what is the largest prime factor of x?

A)2
B)3
C)5
D)7
E)11

src:orbit test prep



Given,

\(x = 2^7^4 - 2^7^0\)

\(x= 2^{70}(2^4 - 1)\)

\(x = 2^{70} 15\)

\(x = 2^{70}*5*3.\)

So, 5 is the largest prime of x.

The best answer is C.
Re: If x = 2^7^4 - 2^7^0, what is the largest   [#permalink] 07 Sep 2018, 19:44
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If x = 2^7^4 - 2^7^0, what is the largest

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