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

10-1 Factors and Greatest Common Factors Objective: To find prime factorizations and greatest common factors for monomials. Standard 11.0

Factors Factor: a number or variable that divides evenly into your original number. Example 1: Find the factors of 72. 1 72 2 36 3 24 4 18 6 12 8 9 This problem is like #19-23 in homework tonight!

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

FACTOR TREE (for composite #s) 384 2 192 2 96 2 48 2 24 2 12 2 6 2 3 2•2•2•2•2•2•2•3 Prime factorization

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

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

Greatest Common Factor (GCF) Make a factor tree and multiply together what they have in common 80 28 2 40 2 14 2 20 2 7 2 10 2 5 2•2 = 4 =GCF

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

Challenge Problem – find the GCF

Homework Greatest Common Factor Worksheet

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

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.

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.

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.

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.

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 