Question

HCF of 144 and 198 is
a) 9
b) 18
c) 6
d) 12

Answer 1

Hint: We have two numbers as 144 and 198. We need to find the HCF of these numbers. So, by the prime factorization 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.

Complete step-by-step solution:
We have the following numbers: 144 and 198
Now, by prime factorization method, we get the prime factors of the numbers:
$\begin{align}
  & 144=2\times 2\times 2\times 2\times 3\times 3 \\
 & 198=2\times 3\times 3\times 11 \\
\end{align}$
So, we need to find the common factors of 144 and 198
We get: $2\times 3\times 3=18$ as a common factor of 144 and 198
Therefore, 18 is the HCF of 144 and 198
Hence, option (b) is the correct answer.

Note: There is an alternate method to find the HCF of given two numbers, i.e. division method. 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. In the given question: the largest number is 198 and the smallest one is 144. Divide 98 by 144.
\[144\overset{1}{\overline{\left){\begin{align}
  & 198 \\
 & 144 \\
 & \overline{\text{ 54 }} \\
\end{align}}\right.}}\]
Take divisor as new dividend and remainder as the new divisor, i.e. divide the first divisor by the first remainder.
\[54\overset{2}{\overline{\left){\begin{align}
  & 144 \\
 & 108 \\
 & \overline{\text{ 36 }} \\
\end{align}}\right.}}\]
Proceed till the remainder is zero and the last divisor will be the HCF of the given numbers
\[36\overset{1}{\overline{\left){\begin{align}
  & 54 \\
 & 36 \\
 & \overline{\text{18 }} \\
\end{align}}\right.}}\]
\[18\overset{2}{\overline{\left){\begin{align}
  & 36 \\
 & 36 \\
 & \overline{\text{ 0 }} \\
\end{align}}\right.}}\]
Therefore, 18 is the HCF of 144 and 198