What is the product of the digits in the base 8 representation of $6543_{10}$?
I need to convert 6543 from base 10 to base 8 first. I can use repeated division by 8 and write down the remainders. 6543 divided by 8 is 817 with a remainder of 7. 817 divided by 8 is 102 with a remainder of 1. 102 divided,by 8 is 12 with a remainder of 6. 12 divided by 8 is 1 with a remainder of 4. 1 divided by 8 is 0 with a remainder of 1. So the base 8 representation of 6543 is 14617. Now I just need to multiply the digits: 1 x 4 x 6 x 1 x 7. That gives me 168. 