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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]  29 Aug 2018, 06:53
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Question Stats:

60% (00:07) correct 40% (00:23) wrong based on 5 sessions
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]  29 Aug 2018, 07:19
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Expert's post
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

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]  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.

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