SOLUTION: What is the units digit of 7^2019?

Algebra.Com
Question 1138837: What is the units digit of 7^2019?
Answer by Edwin McCravy(20063)   (Show Source): You can put this solution on YOUR website!
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
RELATED QUESTIONS

what is the units digit of 7^15? (answered by Alan3354,edjones)
What is the units digit of 3^1 + 3^3 + 3^5 + 3^7 +………+ 3^2009... (answered by Alan3354)
What is the units digit of 3^1001 × 7^1002 × 13^1003... (answered by ikleyn)
7) The units digit of a two-digit number is twice the tens digit. If the square of the... (answered by Edwin McCravy)
Find the units digit of... (answered by MathLover1)
What is the units digit of 10,452^134... (answered by solver91311)
What is the units digit of... (answered by ikleyn)
The tens digit of a number exceeds the units digit by 2. The sum of the digits is 1/7 of... (answered by longjonsilver)
The tens digit of a three digit number is three times the units digit and the units digit (answered by ankor@dixie-net.com)