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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?

 Jan 6, 2019
 #1
avatar+4463 
+2

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

 Jan 6, 2019
 #2
avatar+98173 
+1

Here's another way

217 * 45 =  9765

 

9765 = 1627 (6) R 3

 

3 is the units digit

 

 

cool cool cool

 Jan 6, 2019

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