Answer
The base five Numeral is\[{{24334}_{\text{five}}}\].
Work Step by Step
To convert base ten numeral to any other base,divide provided numeral with the greatest number in the power base value as shown below:
\[625\overset{2}{\overline{\left){\begin{align}
& 1844 \\
& \underline{1250} \\
& \text{ }594 \\
\end{align}}\right.}}\]
Now, divide 594 by 125:
\[125\overset{4}{\overline{\left){\begin{align}
& 594 \\
& \underline{500} \\
& \text{ }94 \\
\end{align}}\right.}}\]
Divide 94 by 25:
\[25\overset{3}{\overline{\left){\begin{align}
& 94 \\
& \underline{75} \\
& 19 \\
\end{align}}\right.}}\]
Divide 19 by 5:
\[5\overset{3}{\overline{\left){\begin{align}
& 19 \\
& \underline{15} \\
& 4 \\
\end{align}}\right.}}\]
Here,base value of resultant numeral is \[5\].So, powers of base numerals are \[{{5}^{0}},\,{{5}^{1}},\,{{5}^{2}},\,{{5}^{3}},....\]which can be written as\[1,\,\,5,\,\,25,\,\,125,\,\,625,....\]when solved.
Now, use the quotients of each division based ten numerals can be found as follows:\[\begin{align}
& 2\times 625\,+4\times 125\,+3\times 25\,+3\times 5+\,4\times 1\,=2\times {{5}^{4\,}}+\,4\times {{5}^{3}}\,+3\times {{5}^{2}}\,+3\times {{5}^{1}}+4\times {{5}^{0}} \\
& ={{24334}_{\text{five}}}
\end{align}\]
The base five Numeral is\[{{24334}_{\text{five}}}\].
