Answer
Required solution is\[{{56}_{\text{seven}}}\].
Work Step by Step
Let's calculate:
First, write the multiples of \[31\] in base seven.
\[\begin{align}
& 31\times 1=31 \\
& 31\times 2=62 \\
& 31\times 3(62+31)=123 \\
& 31\times 4(123+31)=154
\end{align}\]
\[31\times 5(154+31)=215\]
\[31\times 6(215+31)=246...\] ….. (1)
Now, divide the given base seven numerals.
\[\begin{align}
& {{31}_{\text{seven}}}\overset{{{56}_{\text{seven}}}}{\overline{\left){\begin{align}
& {{2426}_{\text{seven}}} \\
& \underline{215} \\
\end{align}}\right.}} \\
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,246 \\
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{246} \\
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{\,\,\,\,\,\,0} \\
\end{align}\]
Here, first divide 242 by 31, highest number less than \[{{242}_{\text{seven}}}\]is \[{{215}_{\text{seven}}}\]from the table of 31.