Question

Find the HCF of the following 27, 63.

Answer 1

Hint:
Here, we have to use the concept of the factorization and HCF. Factorization is the process in which a number is written in the forms of its small factors which on multiplication give the original number. We will factorize both the numbers separately. After the factorization we will take maximum common factors of both the numbers to get the value of the HCF. HCF or Highest Common Factor is the largest factor which is the common divisor of both the numbers.

Complete Step by Step Solution:
Given numbers are 27, 63.
First, we have to find out the factors of the given numbers i.e. 27, 63.
Factors are the smallest numbers with which the given number is divisible and their multiplication will give the original number.
So, factors of the number 27 are \[3 \times 3 \times 3\].
Similarly we will find the factors of the other number i.e. 63.
Factors of the number 63 are \[3 \times 3 \times 7\]
Now, to find out the HCF of the numbers we will take maximum common factors of both the numbers i.e. factor 3 which occurs two times in number 27 and factor 3 which also occurs two times in the number 63. Therefore, we get
HCF of the numbers 27, 63 is equal to \[3 \times 3 = 9\].

Hence, the HCF of the given numbers i.e. 27 and 63 is 9.

Note:
We know that HCF of the numbers is generally less than or equal to the LCM of the number. LCM is the lowest common factor which is exactly divisible by both the numbers. In other words, it is the smallest number which is the multiple of the numbers. Product of the LCM and the HCF of some numbers are equal to the product of the original numbers.