Question

How do you find GCF of $24{\text{ and 36}}$?

Answer 1

Hint:
Here we need to find the factors of $24{\text{ and 36}}$ and then we need to find the greatest factor that is common to both the numbers $24{\text{ and 36}}$ and this is known as the greatest common factor or the highest common factor of these two numbers.

Complete step by step solution:
Here we are given the two numbers which are $24{\text{ and 36}}$ and we need to find its GCF which means Greatest Common Factor.
In simple language we need to find the highest number that can divide both $24{\text{ and 36}}$
This can be made clear with an example:
If we have the numbers $8{\text{ and 12}}$ and we need to find its GCF we just need to write all the factors of both the numbers:
$
  8 = (2)(2)(2) \\
  12 = (2)(2)(3) \\
$
Now in the above two we can see that two $2'{\text{s}}$ are common in both so the GCF will be $(2)(2) = 4$
Similarly we need to apply the same method in the given problem where we need to find the GCF of $24{\text{ and 36}}$
We can write them in the form of their factors as:
$24 = (2)(2)(2)(3)$
$36 = (2)(2)(3)(3)$
Now we have written the numbers $24{\text{ and 36}}$ in form of their factors so we now need to notice all the common factors that are there in $24{\text{ and 36}}$
So we can see that in $24{\text{ and 36}}$ two $2'{\text{s and one 3}}$ is common in both. So to get the greatest common factor of $24{\text{ and 36}}$ we just need to multiply all the common terms present in both and we will be able to get GCF of these two numbers as:
${\text{GCF}} = (2)(2)(3) = 12$

Note:
Here the student must know the difference between the GCF and LCM. As we have come to know that in GCF we need to find the highest number that can divide both the numbers but in LCM we need to find the smallest number that can be divided by both the numbers whose LCM is to be found. For example: LCM of $2{\text{ and 4}}$ is $4$ as it is the smallest number completely divisible by $2{\text{ and 4}}$