Question

Determine the HCF of following pairs by finding factors:

(f) $18$ and $36$

Answer 1

Step 1: Find the factors of $18$ and $36$.

$$\begin{gathered} 1\times 18=18 \\ 2\times 9=18 \\ 3\times 6=18 \end{gathered}$$

As $18$ is divisible by $1,2,3,6,9$ and $18$.

So the factors of $18$ are: $1,2,3,6,9$ and $18$.

$$\begin{gathered} 1\times 36=36 \\ 2\times 18=36 \\ 3\times 12=36 \\ 4\times 9=36 \\ 6\times 6=36 \end{gathered}$$

As $36$ is divisible by $1,2,3,4,6,9,12,18$ and $36$.

So the factors of $36$ are: $1,2,3,4,6,9,12,18$and $36$.

Step 2: Find the HCF of $18$ and $36$.

Factors of $18$ are: $\overline{)1},\overline{)2},\overline{)3},\overline{)6},\overline{)9}$ and $\overline{)18}$.

Factors of $36$ are: $\overline{)1},\overline{)2},\overline{)3},\overline{)4},\overline{)6},\overline{)9},\overline{)12},\overline{)18}$and $36$.

Common factors of $18$ and $36$ are $\overline{)1},\overline{)2},\overline{)3},\overline{)6},\overline{)9}$ and $\overline{)18}$.

Hence, the HCF of $18$ and $36$ is $18$.