Question

What factors do 8 and 12 have in common?

Answer 1

Hint: The factor of a number is defined as a number which divides the given number completely. For example, the factors of 10 are 1, 2, 5 and 10, as they all divide 10 leaving no remainder behind. In order to solve our question, we will first find the factors of 8 and 12 individually and then find out the common factors between them.

Complete step by step answer:
We have to find the factors of 8 and 12 in the given problem. So, let us find their factors one by one.
At first, we can write the factors of 8 as follows:
$\Rightarrow Factors\left( 8 \right)=\left\{ 1,2,4,8 \right\}$
Let us name the above equation as (1), so we have:
$\Rightarrow Factors\left( 8 \right)=\left\{ 1,2,4,8 \right\}$ ......... (1)
Then, we can write the factors of 12 as follows:
$\Rightarrow Factors\left( 12 \right)=\left\{ 1,2,3,4,6,12 \right\}$
Let us name the above equation as (2), so we have:
$\Rightarrow Factors\left( 12 \right)=\left\{ 1,2,3,4,6,12 \right\}$ ......... (2)
Thus, from equation number (1) and (2), we can write the common factors (C.f.) of 8 and 12 as follows:
$\Rightarrow C.f.\left\{ 8,12 \right\}=\left\{ 1,2,4 \right\}$
Here, we can see that 8 and 12 have three common factors. Additionally, the smallest common factor of 8 and 12 is equal to 1 and the greatest common factor of 8 and 12 is equal to 4.

Hence, the factors that are common to both 8 and 12 are 1,2 and 4.

Note: Students often get confused between factors of a number and multiples of a number. A factor exactly divides the given number, whereas a multiple is exactly divisible by the same given number. We can better understand this with the help of the following example:
$\begin{align}
  & \Rightarrow \text{Factors of 9 = }\left\{ 1,3,9 \right\} \\
 & \Rightarrow \text{Multiples of 9 = }\left\{ 9,18,27,36,.......... \right\} \\
\end{align}$