Question

HCF of 6, 72 and 120 is
a) 6
b) 2
c) 3
d) 1

Answer 1

Hint: We have the numbers as 6, 72 and 120. 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: 6, 72 and 120
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:
$\begin{align}
  & 6=2\times 3 \\
 & 72=2\times 2\times 2\times 3\times 3 \\
 & 120=2\times 2\times 2\times 3\times 5 \\
\end{align}$
So, the lowest degree of common prime factors is: ${{2}^{1}},{{3}^{1}}$
So, the product of the lowest degree of prime factors is: \[{{2}^{1}}\times {{3}^{1}}=6\]
Therefore, 6 is the HCF of 6, 72 and 120
Hence, option (a) 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 given numbers. In the given question: the largest number is 120 and the smallest one is 6. Divide 120 by 6
\[6\overset{20}{\overline{\left){\begin{align}
  & 120 \\
 & 120 \\
 & \overline{\text{ 0 }} \\
\end{align}}\right.}}\]
Therefore, 6 is the HCF of 6, 72 and 120