Question

Find the HCF of 12, 24 and 48 by listing factors.

Answer 1

Hint- Here we will proceed by listing all the factors of 12, 24 and 48. Then we will see which of the factors of these three numbers is highest. That highest factor will be known as HCF of 12, 24 and 48.

Complete step-by-step answer:

Since we are going to find HCF, we must know the concept of HCF-
HCF means highest common factor. In other words, we can say that HCF is the greatest number which can divide the given numbers. HCF is also known as GCD.
Firstly, we will find the factors of 12, 24 and 48.
Factors of 12 – 1, 2, 3, 4, 6, 12.
Factors of 24 – 1, 2, 3, 4, 6, 8, 12, 24.
Factors of 48 – 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
As we can see that the highest factor is 48 but it is not common in the other two numbers so it is not the HCF of 12, 24 and 48.
Also 24 is second highest but it is not common in number 12 so it is not the HCF of 12, 24 and 48.
But we can see that the highest common factor between all the three numbers i.e. 12, 24 and 48 is 12.
Therefore, the answer is 12.

Note- While solving this question, we must understand that although one of the given numbers has the highest factor still it cannot be considered as HCF until it is common in all the given numbers. Also one must know that the other name of HCF is GCD therefore whether we are asked GCD or HCF, we have to use the same method only.