Question

What is the GCF of 36 and 60?

Answer 1

Hint: In the above type of question we need to find the GCF of the given two numbers i.e. 36 and 60, it means that we need to find the greatest factor that divides both the numbers until there is no common factor left between them.

Complete step by step solution:
In the above mentioned question we need to find the GCF which is none other than HCF which means highest common factor. Highest common factor, as the name suggests we need to find a factor between the numbers mentioned, this factor should divide all the numbers given. This factor can be made with all the common factors present between the numbers. Let us take an example of 12 and 14 in this we can see that 2 is a factor which will give the remainder as 6 and 7 respectively after dividing the numbers by 2. Now let us take the numbers mentioned in the question which is 36 and 60. To make the calculation easier and faster we will write down the factorization of both the numbers first. So the factorization of 36 is:
$$36=2\times 2\times 3\times 3$$
And the factorization of 60 is:
$$60=2\times 2\times 3\times 5$$
Now we will check in the factorization of the two numbers which all factors are common. So through observation we can see that $$2\times 2\times 3$$ are the common factors between the two numbers mentioned in the question so we these will become the highest common factor between the two terms.
So the highest common factor or the greatest common factor of 36 and 60 is 12.

Note: In the above mentioned question there can be slight mistake between LCM and HCF LCM is just the opposite of HCF and LCM we need to find every single factor of the term to get the LCM of the numbers but in HCF we need to find the factors which are common between those numbers.