Question

Find the HCF of the following numbers:
81 and 243

Answer 1

Hint:We know that the HCF of two numbers is the highest common factor of two numbers which is also called as the greatest common factor or greatest common divisor. So we will use the division method to find the HCF of two numbers.

Complete step-by-step answer:
We have been asked to find the HCF of 81 and 243.
We will use the division method to find the HCF and we will follow the following steps to find the HCF.
(i) We will divide the large number by a small number.
(ii) If the remainder is left, then divide the first divisor by remainder.
(iii) If the remainder divides the first divisor completely, then it is the HCF of two numbers.
(iv) If the remainder does not divide the first divisor completely then we will repeat the steps.
So 81 is a smaller number than 243 so first we will divide 243 by 81 as follows:
\[81\overset{3}{\overline{\left){\begin{align}
  & 243 \\
 & \underline{243} \\
 & \underline{000} \\
\end{align}}\right.}}\]
Here, the remainder is equal to zero means that the 81 divides 243 completely.
Hence 81 is the HCF of 81 and 243.

Note: We can also use the prime factorization method to find the HCF of the given two numbers. Also, remember that highest common factor i.e. HCF is also known as greatest common divisor or greatest common factor. We can solve this by writing down all factors of 81 as well as 243 and then choosing the highest common factors from those. But this is very time consuming to find all the factors and then analyze them.