Question

Determine the HCF of following pairs by finding factors:

$25$ and $30$

Answer 1

Step 1: Find the factors of $25$ and $30$.

$$\begin{gathered} 1\times 25=25 \\ 5\times 5=25 \end{gathered}$$

As $25$ is divisible by $1,5$and $25$.

So the factors of $25$ are: $1,5$ and $25$.

$$\begin{gathered} 1\times 30=30 \\ 2\times 15=30 \\ 3\times 10=30 \\ 5\times 6=30 \end{gathered}$$

As $30$ is divisible by $1,2,3,5,6,10,15$ and $30$.

So the factors of $30$ are: $1,2,3,5,6,10,15$ and $30$.

Step 2: Find the HCF of $25$ and $30$.

Factors of $25$ are: $\overline{)1},\overline{)5}$ and $25$.

Factors of $30$ are: $\overline{)1},2,3,\overline{)5},6,10,15$ and $30$.

Common factors of $25$ and $30$ are $\overline{)1}$ and .$\overline{)5}$

Hence, the HCF of $25$ and $30$ is $5$.