From base ten to base five

Statement

Write the number $213$ (in base ten) in base five.

Solution

Divide repeatedly by $5$, reading the remainders from bottom to top: $\begin{aligned} 213 &= 5\cdot 42 + 3, \ 42 &= 5\cdot 8 + 2, \ 8 &= 5\cdot 1 + 3, \ 1 &= 5\cdot 0 + 1. \end{aligned}$ The remainders from last to first give $(1323)_5$. Check: $1\cdot 125 + 3\cdot 25 + 2\cdot 5 + 3 = 213$. $213 = \boxed{(1323)_5}.$