What is the units digit of 7^2019?
The units digit of 7 is 7
The units digit of 7×7=49 is 9
The units digit of 9×7=63 is 3
The units digit of 3×7=21 is 1
The units digit of 1×7=7 is 7 again.
So the units digits of the
powers of 7 go 7,9,3,1,7,9,3,1,7,9,3,1,...
They go in groups of 4,
504
4)2019
20
19
16
3
The quotient is 504 and the remainder is 3. So the units digit of 72019 will
be the 3rd in the 504th group of four 7,9,3,1, and so it will be 3.
Edwin
