Question

What is the Greatest Common Factor (GCF) of $4$ and $12$ ?

Answer 1

Hint: Here we have to find the Greatest Common Factor (GCF) of the two numbers given. Firstly we will find the prime factors of each number given by using the long division method. Then we will take out the common factors from both the numbers. Finally we will multiply the common factors and get our desired answer.

Complete answer:
We have to find the greatest common factor of the number given below:
$4$ And $12$
Now we will find the prime factors of each number by using the long division method.
Firstly we will find the prime factor of $4$ by dividing it by first prime number that is $2$ and moving on to other prime number till we get the remainder as $1$ as follows:
$\begin{align}
  & 2\left| \!{\underline {\,
  4 \,}} \right. \\
 & 2\left| \!{\underline {\,
  2 \,}} \right. \\
 & \,\,\,1 \\
\end{align}$
So we got the factors as:
$4=2\times 2$……$\left( 1 \right)$
Next we will find the prime factor of $12$ by dividing it by first prime number that is $2$ and moving on to other prime number till we get the remainder as $1$ as follows:
$\begin{align}
  & 2\left| \!{\underline {\,
  12 \,}} \right. \\
 & 2\left| \!{\underline {\,
  6 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3 \,}} \right. \\
 & \,\,\,1 \\
\end{align}$
So we got the factors as:
$12=2\times 2\times 3$….$\left( 2 \right)$
On comparing equation (1) and (2) we get the common factors as follows:
$\Rightarrow 2\times 2$
$\Rightarrow 4$
So we got the answer as $4$
Hence Greatest Common Factor (GCF) of $4$ and $12$ is $4$ .

Note:
Factors of any number when multiplied gives back the number. Greatest common Factor (GCF) is the largest number which is the factor of two or more numbers given. This means the biggest number that divides the given numbers completely with no remainder is known as GCF. Using prime factorization is the most used method for finding GCF.