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y=2^16−1. The greatest prime factor of y is:

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y=2^16−1. The greatest prime factor of y is:  [#permalink]

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New post 15 Feb 2017, 03:28
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

36% (01:48) correct 64% (01:48) wrong based on 105 sessions

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Concentration: Finance, International Business
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Re: y=2^16−1. The greatest prime factor of y is:  [#permalink]

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New post 15 Feb 2017, 05:01
1
2^16-1=(2^8+1)*(2^8-1)=255 *257

257 is prime number

so answer is E
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Re: y=2^16−1. The greatest prime factor of y is:  [#permalink]

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New post 16 Feb 2017, 12:14
1
Bunuel wrote:
y=2^16−1. The greatest prime factor of y is:

A. Less than 6
B. Between 6 and 10
C. Between 10 and 14
D. Between 14 and 18
E. Greater than 18


2^16 - 1 is a difference of two squares; we can factor it as follows:

y = 2^16−1

y = (2^8 - 1)(2^8 + 1)

y = (2^4 - 1)(2^4 + 1)(2^8 + 1)

y = (2^2 - 1)(2^2 + 1)(2^4 + 1)(2^8 + 1)

y = 3 x 5 x 17 x 257

Since 257 is prime, 257 is the largest prime factor of y.

Answer: E
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Re: y=2^16−1. The greatest prime factor of y is:  [#permalink]

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New post 24 Mar 2018, 12:35
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Re: y=2^16−1. The greatest prime factor of y is: &nbs [#permalink] 24 Mar 2018, 12:35
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