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# Factor out the greatest common monomial factor: 15p-3q

Factor out the greatest common monomial factor!!!!!!!!!!!!!!!!!!!

### 1 Answer by Expert Tutors

Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...
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The greatest common factor among a set of terms is the largest factor that will divide evenly into every term.

15p - 3q

Looking at these two terms, we see that they don't share a common variable. This means that no variable can be factored out of both terms. So look at the coefficients of the two terms and find their factors to see if they share any common factors.

factors of 15:     1, 3, 5, 15

factors of 3:      1, 3

The two terms thus share two common factors, those being 1 and 3. The larger of these two common factors is the greatest common among both terms, which means that the greatest common factor here is 3.

When factoring out a 3 from both terms, we see that it does so evenly:

15p  -  3q  =  3*5p  -  3*q  =  3(5p - q)