WAEC 2023 · Paper 1 · Q5

Express $413_7$ in base 5.

Worked solution (try it first)

Change to base ten: $413_7 = 4 \times 49 + 7 + 3 = 206$ .
Divide by 5 repeatedly: $206 = 5 \times 41 + 1$ , $41 = 5 \times 8 + 1$ , $8 = 5 \times 1 + 3$ , and $1 = 5 \times 0 + 1$ .
Read the remainders from the bottom up: $1311_5$ , option B.