Answer
The result on division is\[\text{Quotient}={{41}_{\text{five}}},\text{Remainder }={{1}_{\text{five}}}\].
Work Step by Step
Consider the provided expression\[{{3}_{\text{five}}}\overline{\left){{{224}_{\text{five}}}}\right.}\] , where\[{{3}_{\text{five}}}\] is divisor and \[{{224}_{\text{five}}}\]is dividend.
From the provided multiplication table find the largest product that is less than or equal to\[{{22}_{\text{five}}}\] that is \[{{3}_{\text{five}}}\times {{4}_{\text{five}}}={{22}_{\text{five}}}\]and write \[{{22}_{\text{five}}}\]under the first two digits of dividends and solve further:
\[\begin{align}
& \,\,\,\,\,\,\,\,\,\,\,\,4 \\
& {{3}_{\text{five}}}\overline{\left){{{224}_{\text{five}}}}\right.} \\
& \,\,\,\,\,\,\,\,\,\,\underline{22} \\
& \,\,\,\,\,\,\,\,\,\,00 \\
\end{align}\]
On subtracting \[{{22}_{\text{five}}}-{{22}_{\text{five}}}\]the obtained value is 0. Thus, bring down next dividend\[{{4}_{\text{five}}}\].
From the provided multiplication table observe that \[{{3}_{\text{five}}}\times {{1}_{\text{five}}}={{3}_{\text{five}}}\]which is less than\[{{4}_{\text{five}}}\].Therefore, write \[{{3}_{\text{five}}}\] under the third digit of dividend such as:
\[\begin{align}
& \,\,\,\,\,\,\,\,\,\,\,\,41 \\
& {{3}_{\text{five}}}\overline{\left){{{224}_{\text{five}}}}\right.} \\
& \,\,\,\,\,\,\,\,\,\,\underline{22} \\
& \,\,\,\,\,\,\,\,\,\,\,004 \\
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{3} \\
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1 \\
\end{align}\]
On subtracting\[{{4}_{\text{five}}}-{{3}_{\text{five}}}\] the obtained value is\[{{1}_{\text{five}}}\].
Thus, the obtained result on the division is\[\text{Quotient}={{41}_{\text{five}}},\text{Remainder }={{1}_{\text{five}}}\].
The result on division is\[\text{Quotient}={{41}_{\text{five}}},\text{Remainder }={{1}_{\text{five}}}\].
