Question

Determine the HCF of following pairs by finding factors:

(c) $16$ and $48$

Answer 1

Step 1: Find the factors of $16$ and $48$.

$$\begin{gathered} 1\times 16=16 \\ 2\times 8=16 \\ 4\times 4=16 \end{gathered}$$

As $16$ is divisible by $1,2,4,8$ and $16$.

So the factors of $16$ are: $1,2,4,8$ and $16$.

Also,

$$\begin{gathered} 1\times 48=48 \\ 2\times 24=48 \\ 3\times 16=48 \\ 4\times 12=48 \\ 6\times 8=48 \end{gathered}$$

As $48$ is divisible by $1,2,3,4,6,8,12,16,24$ and $48$.

So the factors of $48$ are: $1,2,3,4,6,8,12,16,24$ and $48$.

Step 2: Find the HCF of $16$ and $48$.

Factors of $16$ are: $\overline{)1},\overline{)2},\overline{)4},\overline{)8}$ and $\overline{)16}$.

Factors of $48$ are: $\overline{)1},\overline{)2},3,\overline{)4},6,\overline{)8},12,\overline{)16},24$ and $48$.

Common factors of $16$ and $48$ are $\overline{)1},\overline{)2},\overline{)4},\overline{)8}$ and $\overline{)16}$.

Hence, the HCF of $16$ and $48$ is $16$.