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\( \Large 2^{16}-1 \) is divisible by
|
A) 11 |
|
B) 13 |
|
C) 17 |
|
D) 19 |
Correct Answer:
| C) 17 |
Description for Correct answer:
\( \Large 2^{16}-1^{16} \)
\( \Large = (2^{8}-1^{8})(2^{8}+1^{8}) \)
\( \Large = (2^{4}-1)(2^{4}+1)(2^{8}+1) \)
\( \Large = (16-1)(16+1)(2^{8}+1) \)
\( \Large = 15 \times 17(2^{8}+1) \)
\( \therefore\Large 2^{16}-1 \) is divisible by 17
\( \Large 2^{16}-1^{16} \)
\( \Large = (2^{8}-1^{8})(2^{8}+1^{8}) \)
\( \Large = (2^{4}-1)(2^{4}+1)(2^{8}+1) \)
\( \Large = (16-1)(16+1)(2^{8}+1) \)
\( \Large = 15 \times 17(2^{8}+1) \)
\( \therefore\Large 2^{16}-1 \) is divisible by 17
Part of solved Number series questions and answers : >> Aptitude >> Number series
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