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Greatest Common Factor

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+48+4 there are three common factors: 8+4=81+418+4=42+228+4=24+14\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 44 because it's the highest factor that exist in both 88 and 4.4. If the expression contains a variable, it can be a part of the GCF. The expression 4x+2x4x+2x has the GCF: 4x+2x=2x2+2x1=2x(2+1). 4x+2x ={\color{#0000FF}{2x}}\cdot 2+{\color{#0000FF}{2x}}\cdot1={\color{#0000FF}{2x}}(2+1).

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