Skill: Factor a common numerical factor from an expression

Explanation and Free Practice Resources

Factoring a common numerical factor rewrites a sum or difference of terms as a product by applying the distributive property in reverse, such as $6x+15=3(2x+5)$ . The factor must divide every term, and the remaining expression records each term’s quotient; choosing the greatest common numerical factor gives a useful simplest form and supports later work with equivalent expressions, equations, and polynomial factoring, without extending to advanced symbolic or multivariable cases.

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Detailed Explanation: Factor a common numerical factor from an expression

To factor out a common numerical factor, find a number that divides every term. It is usually best to choose the greatest common factor (GCF).

Example: Factor $18x+24$ .

Find the GCF of the numerical parts, $18$ and $24$ :

\text{GCF}(18,24)=6

Divide each term by $6$ :

18x\div 6=3x \qquad \text{and} \qquad 24\div 6=4

Write $6$ outside parentheses and the quotients inside:

18x+24=6(3x+4)

Check by distributing $6$ :

6(3x+4)=6\cdot 3x+6\cdot 4=18x+24

Therefore, the factored form is

\boxed{6(3x+4)}

The number outside the parentheses must divide every term in the original expression.

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