Question

How do you find the GCF of 16, 56?

Answer 1

Hint: We are given terms as 16 and 56, we are asked to find the greatest common fraction, 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 16 and 56 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 an answer.

Complete step by step answer:
We are given two terms as 16 and 56, we are asked to find the greatest common factor. We will learn what the greatest common factors mean.
Now greatest common factor means the greatest, biggest possible term that is common to possible terms that is common to all the terms given to us.
It is also known as HCF (Highest-common-factor)
We have 16 and 56 we have to find the number which is common to 16 and 56 to find this 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 that 16 is written as $2\times 2\times 2\times 2$
Whole 56 is written as $2\times 2\times 2\times 7$ we get –
So, $16=2\times 2\times 2\times 2$
$56=2\times 2\times 2\times 7$
We can see that 3 pair of two are common in 16 and 56, so
GCF of 16 and 56 is \[2\times 2\times 2=8\]
That is greater common factor (GCF) is 8
Now we will find the GCF using long division
So,
$\begin{align}
  & \left. {\underline {\,
 16 \,}}\! \right| 56\left| \!{\underline {\,
  3 \,}} \right. \\
 & \text{ 48} \\
 & \text{ }\left. {\underline {\,
 8 \,}}\! \right| 16\left| \!{\underline {\,
  2 \,}} \right. \\
 & \text{ 16} \\
 & \text{ }\times \\
\end{align}$
So the highest common factor is 8 that means greater common factor GCF 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 a prime factor answer will be not visible.
For example:
$8=4\times 2$ and $16=8\times 2$
So we can see only 2 are common. So, a common term can be assumed as 2 and it will become an incorrect option/ answer.