**Finding the Greatest Common Factor**

The numbers 20 and 30 have several factors in common, among them 2 and 5. The greatest of the common factors is called the **greatest common factor, GCF. **One way to find the GCF is by making a list of factors of each number.

List all the factors of 20: 1, 2, 4, 5, 10, and 20.

List all the factors of 30: 1, 2, 3, 5, 6, 10, 15, and 30.

Now list the numbers common to both lists, the common factors: 1, 2, 5, and 10.

Then the greatest common factor, the GCF, is 10, the largest number in the common list.

**IMPORTANT POINTS OF GREATEST COMMOM FACTOR**

**FACTOR AND FACTORIZATION**

**a.** To **factor **a polynomial is to express it as a product.

**b.** A **factor **of a polynomial *P *is a polynomial that can be used to express *P *as a product.

**c.** A **factorization **of a polynomial is an expression that names that polynomial as a product.

**TO FIND THE GCF OF TWO OR MORE MONOMIALS**

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**a.** Find the prime factorization of the coefficients, including _1 as a factor if any coefficient is negative.

**b. **Determine any common prime factors of the coefficients. For each one that occurs, include it as a factor of the GCF. If none occurs, use 1 as a factor.

**c. **Examine each of the variables as factors. If any appear as a factor of all the monomials, include it as a factor, using the smallest exponent of the variable. If none occurs in all the monomials, use 1 as a factor.

**d. **The GCF is the product of the results of steps (b) and (c).