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Factoring – Greatest Common Factor

• When factoring out the greatest common factor (GCF), determine the common factor by looking at the following:

1. Numerical coefficients2. Each variable individually3. Expressions in parentheses

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Example 1:

5 212 18x x

1. Common numerical factor: 6

2. Common variable x: 2x

Therefore, the common factor is 26x

Hint: use the smallest exponent.

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Finish the problem by asking what the common factor would be multiplied by to get the correct term in the original expression.

2 36 (2 )x x

5 212 18x x

2 36 (2 3)x x

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Example 2:

4 3 2 4 28 12 20x y x y xy

1. Common numerical factor: 4

2. Common variable x: x

3. Common variable y: 2y

Therefore, the common factor is 24xy

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4 3 2 4 28 12 20x y x y xy

Finish the problem by asking what the common factor would be multiplied by to get the correct term in the original expression.

2 34 (2 )xy x y

2 3 24 (2 3 5)xy x y xy

2 3 24 (2 3 )xy x y xy

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