Question

what is the remainder you get on dividing 13^23+1 by 12
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Answer 1

Answer:

Unit digit of 12^23 can be determined by dividing power by 4 and knowing its remainder.

23%4= 3

If the remaider was 0 then

For odd last digit, unit digit is 1

For even last digit, unit digit is 6

But here, the remainder is non-zero then last digit of 12= 2 will be raised to the power of the remainder, i.e. , 3.

So, unit digit = 2^3= 8

Similarly, unit digit of 12^13 can be determined as 13%4= 1

So 2^1=2 is the unit digit.

Now 8–1= 7

7%13= 7. Hence, the answer is 7.