The remainder is 2. We only need to know the last digit of 7^381 to know the remainder. last digits are
as you may notice, the last digits repeat every 4 powers, ie., last digit of 7^2 = last digit of 7^6, etc.
381 is one more than 380 (which is divisible by 4), thus 7^381 will have the last digit 7, therefore the remainder will be 2
this is the best approach. first find the pattren, then AC.