Question

Find the HCF of 180, 240 and 360 by long division method.

Answer 1

Hint: First, before proceeding for this, we must know the following division is not the simple type of division as it is continuous division and will not stop until we get remainder as zero. Then, we get the HCF as 120 which is defined as the last divisor which makes the division remainder to be zero is called HCF(Highest Common Factor). Then, by using the above found HCF for the last remaining number which is 120, check whether it is fully divisible by it or not by performing long division again to get the final answer.

Complete step-by-step answer:
In this question, we are supposed to find the HCF of 180, 240 and 360 by long division method.
So, before proceeding for this , we must know the following division is not the simple type of division as it is continuous division and will not stop until we get remainder as zero.
So, by starting the two larger numbers which are 240 and 360 and then dividing them by long division method as:
$240\overset{1}{\overline{\left){\begin{align}
  & \text{ }360 \\
 & -240 \\
 & \text{ }\overline{\text{ 120}}\overset{2}{\overline{\left){\begin{align}
  & 240 \\
 & 240 \\
 & \overline{\text{ 0 }} \\
\end{align}}\right.}} \\
\end{align}}\right.}}$
So, from the above long division done for the last two numbers that is 240 and 360, we get the HCF as 120 which is defined as the last divisor which makes the division remainder to be zero is called HCF(Highest Common Factor).
Now, by using the above found HCF for the last remaining number which is 120, check whether it is fully divisible by it or not by performing long division again.
So, the long division for the number 180 and 120 is:
$120\overset{1}{\overline{\left){\begin{align}
  & \text{ 18}0 \\
 & -120 \\
 & \text{ }\overline{\text{ 60}}\overset{2}{\overline{\left){\begin{align}
  & 120 \\
 & 120 \\
 & \overline{\text{ 0 }} \\
\end{align}}\right.}} \\
\end{align}}\right.}}$
So, from the above calculation is it clear that 60 is the HCF.
Hence, 60 is HCF of the three numbers that are 180, 240 and 360 by long division method.

Note: Now, to solve these types of questions we need to know some of the basics of the HCF and LCM as most of the students confuse them as HCF is the common factor between all the numbers and LCM is the multiplication of the common factors with the remaining ones also. So, most of the time LCM is greater than HCF.