$$\,{2^{16}} - 1$$ is divisible by -
A. 11
B. 13
C. 17
D. 19
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & \Rightarrow {2^{16}} - 1\,\, \cr & = \left( {{2^8} - {1^8}\,\,} \right)\left( {{2^8} + {1^8}\,} \right) \cr & = \left( {{2^4} - 1\,\,} \right)\left( {{2^4} + 1\,\,} \right)\left( {{2^8} + 1\,\,} \right) \cr & = \left( {16 - 1} \right)\left( {16 + 1} \right)\left( {{2^8} + 1\,\,} \right) \cr & = 15 \times 17\left( {{2^8} + 1\,\,} \right) \cr & \therefore {2^{16}} - 1\,\,{\text{is divisible by 17}} \cr} $$Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
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