Question 4.4.9: Dividing in Base 5 Divide 25)1435....

Using the multiplication table for base 5, Table 4.9 on page 190, we list the multiples of the divisor, 2.

2_5 × 1_5 = 2_5

2_5 × 2_5 = 4_5

2_5 × 3_5 = 11_5

2_5 × 4_5 = 13_5

Since 2_5 × 4_5 = 13_5, which is the largest product less than 14_5, 2_5 divides into 14_5 four times. Record the 13. Subtract 13_5 from 14_5. The difference is 1_5. Record the 1.

\\ \ \ \ 4\\ 2_5)\overline{143_5}\\ 13\\ \ \overline{\ \ 1 \ }

Now bring down the 3 as when dividing in base 10.

4\\ 2_5)\overline{143_5} \\ 13\\ \overline{13}

We see that 2_5 × 4_5 = 13_5. Use this information to complete the problem.

44_5\\ 2_5)\overline{143_5}\\ 13\\ \overline{ 13}\\ 13\\ \ \overline{\ \ \ 0}

Therefore, 143_5 ÷ 2_5 = 44_5 with remainder 0_5.