Question : Find the HCF of $\left(4^{315}-1\right)$ and $\left(4^{25}-1\right)$.
Option 1: $1$
Option 2: $\left(4^{25}-1\right)$
Option 3: $1024$
Option 4: $1023$
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Correct Answer: $1023$
Solution : Given numbers: $\left(4^{315}-1\right)$ and $\left(4^{25}-1\right)$ Now, HCF (315, 25) = 5 So, HCF of {(4 315 – 1) and (4 25 – 1)} = ( 4 5 – 1) = 1024 – 1 = 1023 Hence, the correct answer is $1023$.
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