Example 1

Factorise $20+10x$

Solution:

Both 20 and $10x$ can be divided by 10, therefore the Highest Common Factor (HCF) = 10.

$20+10x=10(2+x)\text{take out common factor 10}$

Example 2

Factorise $21ab-14bc$

Solution:

Both $21ab$ and $14bc$ can be divided by 7b, therefore the Highest Common Factor (HCF)= $7b$.

$(21ab-14bc=7b(3a-2c)\text{take out common factor 7b}$

Example 3

Factorise $2a(p-q)-5(p-q)$

Both $2a(p-q)$ and $5(p-q)$  can be divided by $(p-q)$ therefore the Highest Common Factor (HCF) =  $(p-q)$

$2a(p-q)-5(p-q)=(p-q)(2a-5)\text{take out common factor }(p-q)$