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Which of the following is NOT a prime factor of (5^6−2^6)?
A. 3
B. 7
C. 13
D. 17
E. 19
A. 3
B. 7
C. 13
D. 17
E. 19
19 Jan 2014, 09:25
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Mountain14
Apply \(a^2-b^2=(a-b)(a+b)\): \(5^6-2^6=(5^3-2^3)(5^3+2^3)=117*133=(3^2*13)(7*19)\). From the options only 17 is not a prime factor of 5^6−2^6.
Answer: D.
General Discussion
19 Jan 2014, 22:45
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Which of the following is NOT a prime factor of \((5^6 - 2^6)?\)
A. 3
B. 7
C. 13
D. 17
E. 19
\((5^6 - 2^6)\)
\(=(5^3 - 2^3)(5^3 + 2^3)\\
=(5-2)(5^2+5*2+2^2)(5+2)(5^2-5*2+2^2)\\
=3*39*7*19\\
=3*3*13*7*19\)
Answer: (D)
A. 3
B. 7
C. 13
D. 17
E. 19
\((5^6 - 2^6)\)
\(=(5^3 - 2^3)(5^3 + 2^3)\\
=(5-2)(5^2+5*2+2^2)(5+2)(5^2-5*2+2^2)\\
=3*39*7*19\\
=3*3*13*7*19\)
Answer: (D)
