Find the reminder when 8^64 is divided by 63?

(1)1 (b)-1 (c)0 (d) none of these.

Please provide detail solution

We have to find the remainder when 8^64 is divided by 63.

Now, here we have to use primary remainder theorem o find the remainder. since 8 is the remainder when 8 is divided by 63, we proceed further degrees of power.

Now, 8^2 = 64 and here 1 will be the remainder.

Again, 8^3 = 512 and again 8 will be the remainder. In this way, we have the remainders 8, 1, 8, 1, ...................... So, for the 64th degree we can find that the remainder will be 1.

Answer: 1