Question 65

Find the HCF of $$(4^{315} - 1)$$ and $$(4^{25} -1)$$.

Solution

To get the HCF of the given expression, first we need to obtain the HCF of their respective powers.

So HCF of 315 and 25 is 5.

315 = $$5\times7\times9$$

25 = $$5\times5$$

HCF of $$(4^{315} - 1)$$ and $$(4^{25} -1)$$ ==> $$(4^{HCF\ of\ 315\ and\ 25}-1)$$

= $$(4^{5}-1)$$

= (1024-1)

= 1023

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