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Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
What is the largest prime factor ...
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Updated on: 29 Jul 2021, 17:46
Updated on: 29 Jul 2021, 17:46
00:00
Question Stats:
60% (00:52) correct
40% (00:42) wrong based on 5 sessions
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What is the largest prime factor of \(4^{13} + 4^{14} + 4^{15} + 4^{16} \)?
(A) 2
(B) 3
(C) 5
(D) 7
(E) No correct answer
(A) 2
(B) 3
(C) 5
(D) 7
(E) No correct answer
Originally posted by motion2020 on 29 Jul 2021, 17:08.
Last edited by motion2020 on 29 Jul 2021, 17:46, edited 2 times in total.
Last edited by motion2020 on 29 Jul 2021, 17:46, edited 2 times in total.
Re: What is the largest prime factor ...
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29 Jul 2021, 17:26
29 Jul 2021, 17:26
Expert Reply
\(4^{15}(1+1+1+4)\)
\(4^{15}(7)
\)
7 is the answer
\(4^{15}(7)
\)
7 is the answer
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
Re: What is the largest prime factor ...
[#permalink]
29 Jul 2021, 17:29
29 Jul 2021, 17:29
1
Carcass wrote:
\(4^{15}(1+1+1+4)\)
\(4^{15}(7)
\)
7 is the answer
\(4^{15}(7)
\)
7 is the answer
Actually, it is \(4^{13} * (1 + 4 + 16 + 64)\) and \(4^{13} * 85\). Since 85 is divisible by 5 and 17, the largest prime factor is 17. Answer will be E.
