Question

HCF of 168 and 126 is
a) 21
b) 42
c) 14
d) 18

Answer 1

Hint: We have two numbers as 168 and 126. As we know that HCF is the product of the lowest power of prime factors of the given numbers. So, by the prime factorization method, firstly find the factors of all the numbers. Then, multiply the lowest powers of common factors to get the highest common factor or HCF.

Complete step-by-step solution:
We have the following numbers: 168 and 126
Now, write the given natural numbers as the product of prime factors. To obtain the highest common factor multiply all the common prime factors with the lowest degree (power).
Now, by prime factorization method, we get the prime factors of the numbers:
$\begin{align}
  & 168=2\times 2\times 2\times 3\times 7 \\
 & 126=2\times 3\times 3\times 7 \\
\end{align}$
So, the lowest degree of common prime factors is: ${{2}^{1}},{{3}^{1}},{{7}^{1}}$
So, the product of the lowest degree of common prime factors is: \[{{2}^{1}}\times {{3}^{1}}\times {{7}^{1}}=42\]
 Therefore, 42 is the HCF of 168 and 126
Hence, option (b) is the correct answer.

Note: While finding the factors of the numbers, always be careful choosing a prime number as a factor. Because if we choose a composite number, which itself can be factorized further, it makes the solution lengthy. Therefore, always go with prime number, that’s what the prime factorization method means.