Teaching Notes 5.12: Finding the Greatest Common Factor
of Two or More Monomials
Monomials 5.12: Finding the Greatest Common Factor of Two or More
A common mistake students make is to choose the greatest exponent of a common base.- Explain that the greatest common factor of two or more monomials is the common factor
that has the greatest coefficient and the greatest degree in each variable. For example, 6xy^2
is the greatest common factor of 12xy^3 and 18x^2 y^2. 6 is the greatest common factor of the
coefficients 12 and 18, andxy^2 is the greatest common factor ofxy^3 andx^2 y^2. - Review the process of finding the greatest common factor of two or more numbers. Students
will use this skill to find the greatest common factor of the coefficients of each term. - Explain that students must select the smaller exponent of each common factor and each com-
mon variable to find the greatest common factor. For example, if the common factors arex^2
andx^3 , they must choosex^2 becausex^2 is a factor ofx^3. If necessary, expressx^2 asx·xandx^3
asx·x·xto help your students realize thatx^2 is the greatest common factor. - Review the information and example on the worksheet with your students. Work through the
example as a class, noting each step.
EXTRA HELP:
If two or more monomials have no terms in common, the greatest common factor is 1.ANSWER KEY:
(1)x (2) 7 ab^2 (3) 2 x (4)ab (5)a^2 (6) 12 x^2 y^2 (7) 13 (8) 8 xyz
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(Challenge)Sue is incorrect. She should have first simplified (2xy)^2 ,whichis4x^2 y^2 ,andthen
used this term to find the greatest common factor. The greatest common factor isx^2 y.
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