Question

Using Continued Division Method to find the HCF of the numbers $660,1020,1380$

Answer 1

In Continued Division Method we divide the larger number by the smaller number. In the next step we divide the divisor of the first step with the remainder in the first step, and repeat the process until we get $0$ in the remainder. The divisor in the step where we get remainder as $0$ is the HCF

Here we have three numbers i.e, $660,1020,1380$,

Step 1: leave the smallest number first and find the HCF of $1020,1380$

$$\begin{gathered} 1020\overline{)1380}\overline{)1} \\ \underline{-1020} \\ 360\overline{)1020}\overline{)2} \\ \underline{-720} \\ 300\overline{)360}\overline{)1} \\ \underline{-300} \\ 60\overline{)300}\overline{)5} \\ \underline{-300} \\ 0 \end{gathered}$$

here $60$ is the divisor in the last step where the remainder is $0$, hence $HCF=60$

Step 2: Now, in the next step what we do is, we divide the the remaining number i.e, $660$ by the HCF we found in the first step

$$\begin{gathered} 60\overline{)660}\overline{)11} \\ \underline{-60} \\ 60 \\ \underline{-60} \\ 0 \end{gathered}$$

Since $660$ is completely divided by $60$

Hence $HCF$ of $660,1020,1380$ is $60$