Concept

# Greatest Common Factor

The greatest common factor, abbreviated GCF, is the highest factor of all terms in an expression. For example, in the expression $8+4$ there are three common factors: \begin{aligned} 8+4=8\cdot{\color{#0000FF}{1}}+4\cdot{\color{#0000FF}{1}} \\ 8+4=4\cdot{\color{#0000FF}{2}}+2\cdot{\color{#0000FF}{2}} \\ 8+4=2\cdot{\color{#0000FF}{4}}+1\cdot{\color{#0000FF}{4}} \\ \end{aligned} Then, the GCF is $4$ because it's the highest factor that exist in both $8$ and $4.$ If the expression contains a variable, it can be a part of the GCF. The expression $4x+2x$ has the GCF: $4x+2x ={\color{#0000FF}{2x}}\cdot 2+{\color{#0000FF}{2x}}\cdot1={\color{#0000FF}{2x}}(2+1).$