Question

HCF of 36 and 144 is ______
a) 36
b) 144
c) 4
d) 2

Answer 1

Hint: We have two numbers as 36 and 144. We need to find the HCF of these numbers. So, by the division method, we can find the HCF of the given two numbers. In this method divide the largest number by the smallest number among the given numbers until the remainder is zero. The last divisor will be the HCF of the given numbers.

Complete step-by-step solution:
In the given question: the largest number is 144 and the smallest one is 36. Divide 144 by 36.
\[36\overset{3}{\overline{\left){\begin{align}
  & 144 \\
 & 108 \\
 & \overline{\text{ 36 }} \\
\end{align}}\right.}}\]
Take divisor as new dividend and remainder as the new divisor, i.e. divide the first divisor by the first remainder.
\[36\overset{1}{\overline{\left){\begin{align}
  & 36 \\
 & 36 \\
 & \overline{\text{ 0 }} \\
\end{align}}\right.}}\]
Here we get the remainder as 0. Therefore, 36 is the HCF of 36 and 144
Hence, option (a) is the correct answer.

Note: There is an alternate method to find HCF of two numbers, i.e. prime factorization method. In this method, firstly find the factors of all the numbers. Then, find the common factors of all the numbers. That is the highest common factor (HCF) of all the numbers.
We have the following numbers: 36 and 144
Now, by prime factorization method, we get the prime factors of the numbers:
$\begin{align}
  & 36=2\times 2\times 3\times 3 \\
 & 144=2\times 2\times 2\times 2\times 3\times 3 \\
\end{align}$
So, we need to find the common factors of 36 and 144
We get: $2\times 2\times 3\times 3=36$ as a common factor of 36 and 144
Therefore, 36 is the HCF of 36 and 144.