Finding the GCF of a Set of Monomials
Example
Find the GCF of 15w2y, 24w3y2, and -30w2xy.
Solution
Step 1 Write the factorization of each monomial.
| 15w2y 24w3y2
-30w2xy |
= 3 · 5 · w · w · y
= 2 · 2 · 2 · 3 · w · w · w · y · y
= -1 · 2 · 3 · 5 · w · w · x · 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 · w
· w · y
= 3w2y
Thus, the GCF of 15w2y, 24w3y2, and -30w2xy is 3w2y.
To see that 3w2y is a common
factor of 15w2y, 24w3y2, and -30w2xy we write each as a
product using 3w2y as one of
the factors.
| 15w2y 24w3y2
-30w2xy |
= 3w2y · 5
= 3w3y
· 8wy
= 3w2y
· (-10x) |
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