Answer
$31_{\text{four}}$
Work Step by Step
The place values of base four are: $,,,, 4^3, 4^2, 4^1, 1$.
The place value that are less than or equal to $13$ are $4^1$ and $1$
Divide $13$ by $4^1$ or $4$ to obtain:
$13 \div 4 = 3$ remainder $1$
Divide the remainder $1$ by $1$ to obtain:
$1 \div 1 = 1$ remainder $0$
Thus,
$13=(3 \times 4^1) + (1 \times 1)
\\13=31_{\text{four}}$
