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**Tests are graded… Check Aeries! New Homework Stamp Logs Tomorrow **

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Warmups Multiply: Solve the system: 3. 1. Subtract: 2.

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**10-1 Factors and Greatest Common Factors**

Objective: To find prime factorizations and greatest common factors for monomials. Standard 11.0

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Factors Factor: a number or variable that divides evenly into your original number. Example 1: Find the factors of 72. This problem is like #19-23 in homework tonight!

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**Some terms to know Prime: Only factors are 1 & itself**

Composite: Having more than 2 factors Write the prime numbers up to 20: 1, 2, 3, 5, 7, 11, 13, 17, 19

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**FACTOR TREE (for composite #s)**

384 2 24 2 6 2 3 2•2•2•2•2•2•2•3 Prime factorization

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TOO 1) 20 2) 36 2•2•5 2•2•3•3 Hints If it is an even, it is divisible by 2 If you add the digits and the answer is divisible by 3, then the original number is divisible by 3 If it ends in 0 or 5, it is divisible by 5 Stop trying when the answer is smaller than the number you divided by

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**Factoring with Variables**

81b2c3 9 9 3•3•3•3•b•b•c•c•c TOO 32abc3 2•2•2•2•2•a•b•c•c•c

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**Greatest Common Factor (GCF)**

Make a factor tree and multiply together what they have in common 80 28 2 10 2 5 2•2 = 4 =GCF

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**GCF: Biggest number that will divide evenly into all of the numbers**

With variables, take the smallest exponent 32xy2z, 48x3y4 2•2•2•2•2, 2•2•2•2•3 GCF: 16xy2 TOO for Homework 18xp2, 48x4

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**Challenge Problem – find the GCF**

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Homework Greatest Common Factor Worksheet

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Math Lab Warmups Multiply: 3. 1. Subtract: 2.

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**Example 1: Using a Factor Tree to Find Prime Factorization**

Course 2 10-1 Prime Factorization Example 1: Using a Factor Tree to Find Prime Factorization Write the prime factorization of the number. A. 24 Write 24 as the product of two factors. 24 8 · 3 Continue factoring until all factors are prime. 4 · 2 · 3 2 · 2 · 2 · 3 The prime factorization of 24 is 2 · 2 · 2 · 3. Using exponents, you can write this as 23 · 3.

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**Example 2: Using a Factor Tree to Find Prime Factorization**

Course 2 10-1 Prime Factorization Example 2: Using a Factor Tree to Find Prime Factorization Write the prime factorization of the number. B. 150 150 Write 150 as the product of two factors. 30 · 5 Continue factoring until all factors are prime. 10 · 3 · 5 2 · 5 · 3 · 5 The prime factorization of 150 is 2 · 3 · 5 · 5, or 2 · 3 · 52.

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**Insert Lesson Title Here**

Course 2 2-4 Prime Factorization Insert Lesson Title Here Try This: Example 3 Write the prime factorization of the number. A. 36 Write 36 as the product of two factors. 36 18 · 2 Continue factoring until all factors are prime. 9 · 2 · 2 3 · 3 · 2 · 2 The prime factorization of 36 is 2 · 2 · 3 · 3. Using exponents, you can write this as 22 · 32.

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**Insert Lesson Title Here**

Course 2 10-1 Prime Factorization Insert Lesson Title Here Try This: Example 4 Write the prime factorization of the number. B. 90 90 Write 90 as the product of two factors. 45 · 2 Continue factoring until all factors are prime. 9 · 5 · 2 3 · 3 · 5 · 2 The prime factorization of 90 is 3 · 3 · 5 · 2, or 2 · 32 · 5.

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**Your turn! Prime Factorization Worksheet**

Use scratch paper to make your factor trees. Remember to list your factors in order from least to greatest. Work Individually Switch and grade when everyone is done

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