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# 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.

 15w2y24w3y2 -30w2xy = 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 = 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.

 15w2y24w3y2 -30w2xy = 3w2y Â· 5 = 3w3y Â· 8wy = 3w2y Â· (-10x)
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