Question

units digit in 7 powered 105  ?

Answer 1

7^1 = 7
7^2 = 9; last digit when you multiply previous last digit 7*7 = 9
7^3 = 3; last digit when you multiply previous last digit 7*9 = 3
7^4 = 1; last digit when you multiply previous last digit 7*3 = 1
7^5 = 7; " " " " " " " 7*1 = 7
7^6 = 9; " " " " " " " 7*7 = 9

7^7 = 3; " " " " " " " 7*9 = 3
7^8 = 1; " " " " " " " 7*3 = 1
7^9 = 7; " " " " " " " 7*1 = 7
7^10= 9; " " " " " " " 7*7 = 9
:
Can you see the pattern here? repeats after every 4th power
:
Using long diviion, find the remainder 197/4; that would be 1
Therefore the last digit should be 7