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# What is different about factoring with a common factor and factoring by the greatest common factor?

If you factor by the greatest common factor, you can be assured that there are no common factors left. That is not the case if factoring is by an ordinary common factor.

For example,

3 is a common factor of 30 and 36. 30/36 = 10/12.

But 10 and 12 have a common factor: 2.

6 is the GCF of 30 and 36 and 30/36 = 5/6. 5 and 6 have no common factor (other than 1). Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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When you divide 2 or more numbers by a common factor which is not the greatest common factor, they will still have a common factor which is greater than 1. When you divide them by their greatest common factor, the quotients are coprime - that is, they no longer have a factor in common other than 1. Factoring with a common factor will not get you the simplest form, factoring with the GCF will.  Earn +20 pts
Q: What is different about factoring with a common factor and factoring by the greatest common factor?
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