Question 1138837
What is the units digit of 7^2019?
<pre>
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,

 <u>  504</u>
4)2019
  <u>20</u>
    19
    <u>16</u>
     3

The quotient is 504 and the remainder is 3. So the units digit of 7<sup>2019</sup> will 
be the 3rd in the 504th group of four 7,9,3,1, and so it will be 3.

Edwin</pre>