Question

How do you factor out the gcf of $3a+6$ ?

Answer 1

Hint: In this question, we have to find the factors of a given expression. Thus, we will use the greatest common factor method to get the solution. First, we will find the factors of all the three terms in the given expression. After that, we will find the greatest common factor of all the three terms and take common among all. In the end, we will put the remaining terms in the bracket, to get the required solution for the problem.

Complete step by step answer:
According to the problem, we have to find the factors of the given expression.
Thus, we will use the greatest common factor rule to get the solution.
The expression given to us is $3a+6$ -------- (1)
Now, we will first find the factors of all the three terms, that is 3, a, and 6, we get
$3=1\times 3$
$a=1\times a$
$6=1\times 2\times 3$
Thus, we will put the above values in equation (1), we get
$\Rightarrow \left( 1\times 3 \right)\left( 1\times a \right)+\left( 1\times 2\times 3 \right)$
On further simplify the above expression, we get
$\Rightarrow \left( 1\times 3\times a \right)+\left( 1\times 2\times 3 \right)$
Now, we see that 1 and 3 is common in both the terms, that is after and before the (+) sign, therefore we will take common 1 and 3 in the above expression, we get
$\Rightarrow 1\times 3\left( \left( a \right)+\left( 2 \right) \right)$
On solving on the above expression, we get
$\Rightarrow 3\left( a+2 \right)$ which is the required solution.

Therefore, the factors out of the greatest common factor of $3a+6$ is equal to $3\left( a+2 \right)$.

Note: While solving this problem, do mention all the steps carefully to avoid mathematical errors. To check your solution, apply the distributive property $a\left( b+c \right)=ab+ac$ in the answer, to get the expression given in the problem. If it is equal to the expression, the solution is correct otherwise you have made a mistake.