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

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Manager
Joined: 24 Feb 2020
Posts: 165
Location: Italy
WE: Analyst (Investment Banking)
What is the greatest prime factor of 2^13+2^11 - 10 ?  [#permalink]

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15 Apr 2020, 08:59
2
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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
Intern
Joined: 25 Oct 2019
Posts: 27
Re: What is the greatest prime factor of 2^13+2^11 - 10 ?  [#permalink]

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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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Director
Joined: 24 Oct 2015
Posts: 512
Location: India
Schools: Sloan '22, ISB, IIM
GMAT 1: 650 Q48 V31
GPA: 4
What is the greatest prime factor of 2^13+2^11 - 10 ?  [#permalink]

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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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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)

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