Question

What is the GCF of 32 and 36?

Answer 1

Hint: In this question we need to find the GCF of the given two numbers i.e. 32 and 36, in this we have to find the greatest factor that divides both the numbers and as the name suggests after calculating this factor there should not be any common factor left between the two terms.

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 32 is:
\[32=2\times 2\times 2\times 2\times 2\]
Now we will check in the factorization of the two numbers which all factors are common. So through observation we can see that \[2\times 2\] 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 32 and 36 is 4.

Note: In the above mentioned question we can make slight mistake which can happen due to a little confusion between LCM and HCF as both of them have the same working take out the factors to the numbers and then use the common factors to find the answer, to differentiate between this try to remember the first names i.e. least and highest, highest being what we solved above and least being just the opposite.