Answer
\[{{354}_{seven}}\]
Work Step by Step
To multiply two numbers those are not of base 10, follow the below steps,
To multiply such numbers, multiply just as it is done in base ten. That is first multiply the right most column numbers and continue same as it is done for base ten but in base seven there are only 0,1,2, 3, 4, 5 and 6, if multiplication exceeds, 6 then change it in base seven.
\[\begin{align}
{{43}_{seven}} & \\
\times {{6}_{seven}} & \\
\end{align}\]
To solve this, follow the steps,
\[\begin{align}
& {{3}_{seven}}\times {{6}_{seven}}={{18}_{ten}} \\
& {{4}_{seven}}\times {{6}_{seven}}={{24}_{ten}} \\
\end{align}\]
And here 18 and 24 are not in base 7, so convert it.
\[{{18}_{ten}}=\left( 7\times 2 \right)+\left( 4\times 1 \right)={{24}_{seven}}\]
As, 2 is the carry so add 2 in 24, that is \[24+2=26\]
\[{{26}_{ten}}=\left( 7\times 3 \right)+\left( 5\times 1 \right)={{35}_{seven}}\]
\[\begin{align}
& \underline{\begin{align}
{{43}_{seven}} & \\
\times {{6}_{seven}} & \\
\end{align}} \\
& \underline{{{354}_{seven}}} \\
\end{align}\]
So, here is the solution of the multiplication.
