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Suppose that N can be written in base 6 as \(531340_6\) and in base 8 as \(124154_8\). In base 10, what is the remainder when N is divided by 210? Please help.

 Mar 9, 2021
 #1
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well this isn't a good way to solve the problem and I'm sure there's many other smarter ways to solve it, but
 

\(531340_6 = 5(6^5)+3(6^4)+6^3+3(6^2)+4(6)= 38880+3888+ 216+108+24 = 43116_{10}\).

 

the remainder of that when divided by 210 is 66.

 Mar 9, 2021

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