Question

Find HCF by successive division method: 216, 270, 306.

Answer 1

Hint: We first explain the process of successive division methods
 for finding the HCF. We continue the division and find the final divisor. The last one becomes the HCF of the given numbers.

Complete step-by-step answer:
For the successive division method to find HCF, we first need to arrange the given numbers in ascending order.
Then we need to divide the second lowest number by the lowest number. If there is remainder, we keep continuing the division of the previous divisor by the remainder of the same division. We stop when the division gives 0 as remainder.
We take the divisor of the last division and proceed dividing the next number and keep continuing the same process again. The last possible divisor after the completion of all the division becomes the HCF of the numbers.
For our given numbers 216, 270, 306, the order is already there.
We divide 270 by 216.
$216\overset{1}{\overline{\left){\begin{align}
  & 270 \\
 & \underline{216} \\
 & 54 \\
\end{align}}\right.}}$
Now we divide last divisor 216 with the remainder 54.
$54\overset{4}{\overline{\left){\begin{align}
  & 216 \\
 & \underline{216} \\
 & 0 \\
\end{align}}\right.}}$
Now we divide next number 306 by 54.
$54\overset{5}{\overline{\left){\begin{align}
  & 306 \\
 & \underline{270} \\
 & 36 \\
\end{align}}\right.}}$
Now we divide last divisor 54 with the remainder 36.
$36\overset{1}{\overline{\left){\begin{align}
  & 54 \\
 & \underline{36} \\
 & 18 \\
\end{align}}\right.}}$
We divide last divisor 36 with the remainder 18.
$18\overset{2}{\overline{\left){\begin{align}
  & 36 \\
 & \underline{36} \\
 & 0 \\
\end{align}}\right.}}$
Therefore, the HCF of the numbers 216, 270, 306 is 18.
So, the correct answer is “18”.

Note: We need to be careful about choosing the divisor and the dividend. The remainder becomes the divisor of the next division. The remainder and the divisor are the main thing of reducing HCF which comes from the remainder theorem.