Factors are numbers or variables that we can multiply together to get another number or variable expression.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
And, the ability to identify all the factor pairs that make up each term is how we find the Greatest Common Factor (GCF).
The GCF is the greatest number, variable, or combination of numbers and variables that all terms have in common.
In other words, we are looking for the biggest thing they all share, and then we’re going to pull it out!
How?
Ok, so first let’s remember that a monomial is just one term that is either a number, variable, or a product of a number and one or more variables.
Cancellation Property of Quotients
And, the phrase “pulling out the GCF” or “factor out the GCF” simply means that after you have found the greatest number and/or variable that each term has in common, you divide each term of the polynomial by this common factor and write it as a product.
The best thing about pulling out monomial factors is that you have been doing for quite some time without even realizing it!
Every time we reduce fractions and use our cool technique of “I Heart Division,” we are factoring out the GCF.
Math is Fun quips that the GCF is the “greatest” thing for simplifying fractions, and it’s true. When we factor our the GCF all we are doing is reducing or simplifying our polynomial, just like we do for fractions.
So, don’t worry, this is going to be fun!
Finding Greatest Common Factors – Video
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