Here are the steps required to Factor Out the Greatest Common Factor:

Step 1: Determine the greatest common factor of the given terms. The greatest common factor or GCF is the largest factor that all terms have in common. Do not confuse the GCF with the Least Common Denominator (LCD) which is the smallest expression that all terms go into, rather than the greatest number the terms have in common.
Step 2: Factor out (or divide out) the greatest common factor from each term. You could check your answer at the point by distributing the GCF to see if you get the original question. Factoring out the GCF is the first step in many factoring problems.

Example 1 – Factor: 16x2 – 12x

Step 1: Determine the greatest common factor of the given terms. The greatest common factor or GCF is the largest factor that all terms have in common.
Step 1
Step 2: Factor out (or divide out) the greatest common factor from each term.
Step 2

Example 2 – Factor: 12x5 – 18x3 – 3x2

Step 1: Determine the greatest common factor of the given terms. The greatest common factor or GCF is the largest factor that all terms have in common.
Step 1
Step 2: Factor out (or divide out) the greatest common factor from each term.
Step 2

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Example 3 – Factor: 15x3y2 + 10x2y4

Step 1: Determine the greatest common factor of the given terms. The greatest common factor or GCF is the largest factor that all terms have in common.
Step 1
Step 2: Factor out (or divide out) the greatest common factor from each term.
Step 2

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Example 4 – Factor: 22x5y7 – 14x3y8 + 18x6y4

Step 1: Determine the greatest common factor of the given terms. The greatest common factor or GCF is the largest factor that all terms have in common.
Step 1
Step 2: Factor out (or divide out) the greatest common factor from each term.
Step 2

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Example 5 – Factor: x5 + 7x4y3 – 8xy4 + 14xy

Step 1: Determine the greatest common factor of the given terms. The greatest common factor or GCF is the largest factor that all terms have in common.
Step 1
Step 2: Factor out (or divide out) the greatest common factor from each term.
Step 2

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