Factoring using GCF Tuesday August 14th 2012

GCF Greatest Common Factor

What is a factor? Lets look at the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

What is a factor? You list the factors of 12: 1, 2, 3, 4, 6, 12

What are the common factors of 12 and 36? 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 12: 1, 2, 3, 4, 6, 12 Of these factors, which is the greatest or the GCF?

Example 1 Find the GCF of 30 and 42 common factor is a whole number that is a factor of each number. greatest common factor (GCF) is the greatest of their common factors. Example 1 Find the GCF of 30 and 42

Caution: Do not confuse GCF with LCM. A multiple of a whole number is the product of the number and any nonzero whole number. A common multiple of two or more whole numbers is a multiple of each number. The least common multiple (LCM) of two or more whole numbers is the least of their common multiples. Example 2 Find the LCM of 10 and 15

Now lets apply GCF to polynomials: Example 3 Given the polynomial 2x + 10, determine the GCF.

Now lets apply GCF to polynomials: Given the polynomial 6x-2y, determine the GCF.

Now lets apply GCF to polynomials: Given the polynomial 2x2 + 6x, determine the GCF.

Now lets apply GCF to polynomials: Given the polynomial Find the GCF of 40a2b and 48ab4, determine the GCF.

Determine the GCF for each of the following: 1. 2. 3. 4. 5.

Now let’s factor Example 4 Factor 7x+14 using the GCF

Factor 9x - 33 using the GCF

Factor x2 + 8x using the GCF

Example 5 Factor using GCF

Factor these on your own looking for a GCF. 6. 7. 8.