The base-10 numbers 217 and 45 are multiplied. The product is then written in base-6. What is the units digit of the base-6 representation?
217=216+1 = (36)6 + 1
45 = 42+3 = (7)6 + 3
217 x 45 = (216+1)(42+3) = (216)(42)+(216)(3)+42+3 mod 6 = 3
3 is the units digit of 217d x 45d written in base 6
Here's another way
217 * 45 = 9765
9765 = 1627 (6) R 3
3 is the units digit
