1. Essential Question & Warm Up Essential Question: How do you factor a number? Big Idea: Why is it important to know how to factor a number? Warm Up: NOTHING!!

2. Greatest Common Factors with Polynomials Lesson 10 – 1 Page 558 - 563

3. What is a Prime number? A prime number is a whole number that only has two factors: 1 and itself. Example: 13 13 only has 2 factors 1 × 13 = 13 And it cannot be factored down any further than that.

4. Factorization of a Prime Number This tells us that 13 has no other factor other than itself and one. 13 1

5. What is a Composite number? A composite number is a whole number greater than one that has more than two factors. Example: 100 Has more than 2 factors. 2 × 50 = 1004 × 25 = 100 1 ×100=100

6. Factoring of a Composite Number 100 10 52 52 This tells us that the number 100 is composite. Final factors are 5² ×2²

7. GCF GCF stands for Greatest Common Factor. GCF is the greatest number that is a factor of all the integers.

8. Example The factorization for the two numbers is 632 = 2×2×2×79 948 = 2×2×3×79 Take the factors that both numbers have in common and multiply them to get your Greatest Common Factor 2×2×79 = 316 = GCF 632 4 22 158 279 948 7912 4 22 3

9. Factoring Polynomials – using GCF 60a² And 24a³ After you factor them out, you write out the factors they have in common and multiply, giving you the GCF 2²a² = GCF 60a² 6 32 10 52 aa 24a³ 6 32 4 22 aaa

10. Practice Problems Find the GCF of: 180 and 54 Find the GCF of: 260 and 920 Find the GCF of: 32 and 20 Find the GFC of: 34at² and 62a²t¹² Find the GCF of: 565a² and 797a²p² Find the GCF of: 64a² and 92a²