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What is the greatest prime factor of 2^(10)*5^4 - 2^(13)*5^2 + 2^(14)?
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24 Aug 2021, 05:09
24 Aug 2021, 05:09
Expert Reply
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Question Stats:
53% (01:42) correct
46% (01:53) wrong based on 13 sessions
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What is the greatest prime factor of \(2^{10}*5^4 - 2^{13}*5^2 + 2^{14}\)?
(A) 2
(B) 3
(C) 7
(D) 11
(E) 13
(A) 2
(B) 3
(C) 7
(D) 11
(E) 13
Re: What is the greatest prime factor of 2^(10)*5^4 - 2^(13)*5^2 + 2^(14)?
[#permalink]
26 Aug 2021, 13:41
26 Aug 2021, 13:41
can anyone help me with the solution?
Thank you
Thank you
Re: What is the greatest prime factor of 2^(10)*5^4 - 2^(13)*5^2 + 2^(14)?
[#permalink]
26 Aug 2021, 19:22
26 Aug 2021, 19:22
1
\(2^{10}*5^4 - 2^{13}*5^2 + 2^{14}\)
Taking \(2^{10}\) common
\(2^{10} (5^4 - 2^3*5^2 + 2^{4})\)
\(2^{10}(625 - 200 + 16)\)
\(2^{10}(441)\)
\(2^{10}(7 * 7 * 3 * 3)\)
The greatest prime factor \(= 7\)
Answer C
Taking \(2^{10}\) common
\(2^{10} (5^4 - 2^3*5^2 + 2^{4})\)
\(2^{10}(625 - 200 + 16)\)
\(2^{10}(441)\)
\(2^{10}(7 * 7 * 3 * 3)\)
The greatest prime factor \(= 7\)
Answer C
arjunbir wrote:
can anyone help me with the solution?
Thank you
Thank you
