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!!

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Objectives The student will be able to: 1. find the prime factorization of a number. 2. find the greatest common factor (GCF) for a set of monomials.

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Presentation transcript:

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!!

Greatest Common Factors with Polynomials Lesson 10 – 1 Page

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

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

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=100

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

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

Example The factorization for the two numbers is 632 = 2×2×2× = 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

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 aa 24a³ aaa

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