The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 5.12: FINDING THE GREATEST COMMON FACTOR

OF TWO OR MORE MONOMIALS

-------------------------------------------------------------------------------------

The greatest common factor is the largest factor that two or more monomials have in

common. To find the greatest common factor of two monomials, follow the steps below:

1. Use exponents to write the prime factorization of each coefficient.


2. Find the prime numbers that are common factors of each coefficient.


3. Choose the smaller exponent of each common prime number and the smaller exponent
   of each common variable.


4. Find the product of the common factors to find the greatest common factor.

EXAMPLE

Find the greatest common factor of 20 a^2 bc^3 and 30 a^5 b^2.

20 a^2 bc^3 = 22 × 5 ×a^2 ×b×c^330 a^5 b^2 = 2 × 3 × 5 ×a^5 ×b^2

Common factors are 2, 5,a,andb.

1 is the smallest exponent of 2, 5, andb.

2 is the smaller exponent ofa.

The greatest common factor of 20 a^2 bc^3 and 30 a^5 b^2 is 2 × 5 ×a^2 ×bor 10 a^2 b.

DIRECTIONS: Find the greatest common factor of each pair of monomials.

1. 3 x^2 ,2x 2. 7 a^2 b^2 ,14ab^3 c


2. 12 xy,10x 4. 15 ab,7a^2 b^2


3. 9 a^2 ,16a^3 6. 36 x^2 y^2 ,12x^2 y^2


4. 13 a,26b^2 8. 32 xyz^4 ,8xy^2 z

CHALLENGE:Sue tried to find the greatest common factor ofx^2 yand (2xy)^2.

She looked at the common variablesxandyandusedthesmallerexponent

of both variables. She concluded that the greatest common factor isxy.Is

she correct? Explain your reasoning.

199

Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.