SOLUTION: When a positive integer n is divided by 6, the remainder is 2. What is the remainder when 7n is divided by 3? Please explain how I could approach and solve this, thanks!

Question 474908: When a positive integer n is divided by 6, the remainder is 2. What is the remainder when 7n is divided by 3?
Please explain how I could approach and solve this, thanks!
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Note that n ≡ 2 (mod 3) because n can equal anything in {2, 8, 14, ...} and all of these numbers are 2 modulo 3. If n ≡ 2 (mod 3) then 7n ≡ 14 ≡ 2 (mod 3) (hence, the remainder is 2).

Try this with various values of n and you will see that the remainder is always 2.
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