Question

How do you find the GCF of the numbers 8, 16?

Answer 1

Hint: We are given terms as 8 and 16, we are asked to find the greatest common factor, we will first learn what greater factors mean then we will learn about possible techniques that are there to help us in finding the greatest common factor.
We will use the prime factorization method, we factor 8 and 16 and look for the greatest term that is the same in both the digits. We grab those terms and the product of all such terms will be our answer.

Complete step by step answer:
We are given two terms as 8 and 16, we are asked to find the greatest common factor. We will learn what the greatest common factor means.
Now,
Greatest common factor means the greatest, biggest possible term that is common to all the terms given to us.
It is also known as HCF (Highest-common-factor)
We have 8 and 16. We have to find the number which is common to 8 and 16 to find the HCF or greatest common factor.
We have different ways.
1, Factor method
2, Long division method
We will find our answer using both methods to learn more methods.
First we use the factor method.
In this method we write the given term into its prime factor and then look for all possible common terms, we club them and the product of these will be our HCF or greatest common factor.
We know ‘8’ is written as product of $2\times 2\times 2$ while 16 is written as product of four ‘2’, so we get –
$8=2\times 2\times 2$
$16=2\times 2\times 2\times 2$
So, we can see that 16 and 8 both have 3 pairs of two as common.
So, 16 and 8 has common factor as $2\times 2\times 2=8$
Simplifying, we get –
$2\times 2\times 2=8$
So, the greatest common factor of 8 and 16 is 8.

Hence, we get the greatest common factor using long term in 8 and 16 is 8.

Note: While finding the greatest common factor we must factor into the prime factor only then can we find the correct answer if we do not find the prime factor answer will be not visible.
For example,
$8=4\times 2$ and $16=8\times 2$
So, we can see only 2 is common, so a common term one can assume as ‘2’ and it will become an incorrect option/answer.