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# What is the greatest common factor?

How do you know when you have found the greatest one? Demonstrate with an example? Provide a polynomial for your classmate to factor out a monomial

### 1 Answer by Expert Tutors

Efe M. | Licensed Energetic, Creative, and Motivational Math TeacherLicensed Energetic, Creative, and Motiva...
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Hi Jason,

When looking for the greatest common factor among two numbers the easiest way to know that you have found the greatest one is to just list out all the common factors among the two numbers and choose the greatest one.

Example:

• Factors of 18 -> 1,2,3,6,9,18  Factors of 24 --> 1,2,3,4,6,8,12,24
• Common factors between the two --> 1,2,3,6
• 6 is therefore the greatest common factor between 18 and 24.

When simplifying polynomials, you need to find the greatest common factor in order to reduce the numbers down to their simplest forms.

Example:

• Simplify 18x + 24.
• Since we found above that the greatest common factor of 18 and 24 is 6, the response will be:
• 6(3x + 4). It has been reduced to its simplest form.

Hope this helps!