If $3^{2019}$ is divided by 10, then what is the remainder?
If $3^{2019}$ is divided by 10, then what is the remainder?
1
3
7
9
Solution
The unit digits of powers of 3 cycle with period 4: $3^1 = 3$, $3^2 = 9$, $3^3 = 27$, $3^4 = 81$, then repeats. Dividing 2019 by 4 gives remainder 3, so $3^{2019}$ has the same unit digit as $3^3$, i.e. 7. When divided by 10 the remainder equals the unit digit, so the remainder is 7.