Finding the GCF of a Set of Monomials
Example
Find the GCF of 15w^{2}y, 24w^{3}y^{2}, and 30w^{2}xy.
Solution
Step 1 Write the factorization of each monomial.
15w^{2}y 24w^{3}y^{2}
30w^{2}xy 
= 3 Â· 5 Â· w Â· w Â· y
= 2 Â· 2 Â· 2 Â· 3 Â· w Â· w Â· w Â· y Â· y
= 1 Â· 2 Â· 3 Â· 5 Â· w Â· w Â· x Â· y 
Step 2 List each common factor the LEAST number of times it appears
in any factorization.
The common factors are 3, w, and y.
The least number of times that 3 appears in a factorization is once.
So, 3 appears once in the list.
The least number of times that w appears in a factorization is twice.
So, w appears twice in the list.
The least number of times that y appears in a factorization is once.
So, y appears once in the list.
Here is the list: 3, w, w, y
Step 3 Multiply the factors in the list. 3 Â· w
Â· w Â· y
= 3w^{2}y
Thus, the GCF of 15w^{2}y, 24w^{3}y^{2}, and 30w^{2}xy is 3w^{2}y.
To see that 3w^{2}y is a common
factor of 15w^{2}y, 24w^{3}y^{2}, and 30w^{2}xy we write each as a
product using 3w^{2}y as one of
the factors.
15w^{2}y 24w^{3}y^{2}
30w^{2}xy 
= 3w^{2}y Â· 5
= 3w^{3}y
Â· 8wy
= 3w^{2}y
Â· (10x) 
