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What is the greatest prime factor of 2^13+2^11 - 10 ?

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What is the greatest prime factor of 2^13+2^11 - 10 ?  [#permalink]

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New post 15 Apr 2020, 08:59
2
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A
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D
E

Difficulty:

  55% (hard)

Question Stats:

68% (03:01) correct 32% (02:11) wrong based on 34 sessions

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What is the greatest prime factor of \(2^{13}+2^{11} - 10\) ?

(A) 13
(B) 19
(C) 23
(D) 29
(E) 31
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Re: What is the greatest prime factor of 2^13+2^11 - 10 ?  [#permalink]

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New post 15 Apr 2020, 09:09
1
solve the stem and we will get...10*1023

1023 is divisible by 31

so greatest prime factor 31
ans E

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What is the greatest prime factor of 2^13+2^11 - 10 ?  [#permalink]

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New post Updated on: 17 Apr 2020, 04:45
Ravixxx wrote:
What is the greatest prime factor of \(2^{13}+2^{11} - 10\) ?

(A) 13
(B) 19
(C) 23
(D) 29
(E) 31


\(2^{13}+2^{11} - 10\) = \(2^{11}(2^{2}+1) - 10\)
\(2^{11}(5) - 10\) = \(10*1023\)=10*31*11
Ans: E

Originally posted by ArunSharma12 on 15 Apr 2020, 09:09.
Last edited by ArunSharma12 on 17 Apr 2020, 04:45, edited 1 time in total.
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What is the greatest prime factor of 2^13+2^11 - 10 ?  [#permalink]

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New post 17 Apr 2020, 03:27
Ravixxx wrote:
What is the greatest prime factor of \(2^{13}+2^{11} - 10\) ?

(A) 13
(B) 19
(C) 23
(D) 29
(E) 31


Simplifying, we have:

2^11(2^2 + 1) - 10

2^11(5) - 10

5(2^11 - 2)

5(2,048 - 2)

5(2,046) = 5(2 x 1,023) = 5(2 x 3 x 341) = 5(2 x 3 x 11 x 31)

Answer: E
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What is the greatest prime factor of 2^13+2^11 - 10 ?   [#permalink] 17 Apr 2020, 03:27

What is the greatest prime factor of 2^13+2^11 - 10 ?

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