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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