Powerful Finale
Weekly Problem 24 - 2017
What is the last digit of $3^{2011}$?
What is the last digit of $3^{2011}$?
Problem
What is the last digit of $3^{2011}$?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: $7$
To find the next power of $3$, multiply by $3$
To find the last digit of the next power of $3$, multiply the last digit by $3$
$3^1 = 3$ $3^5 = ...3$, since $1\times3=3$
$3^2=9$ $3^6=...9$, since $3\times3=9$
$3^3=...7$ $3^7=...7$ $3^{2011}= ...7$
$3^4=...1$, since $7 \times 3 = 21$ $3^8=...1$ $3^{2012}= ...1$