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Common Factors *Identify Common Factors of a Set of Whole Numbers 5.3D *Identify Prime & Composite Numbers using Patterns in Factor Pairs 5.5B

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Reasoning Mind Academy: Common Factors REMEMBER: A is the answer to a multiplication problem. Key Words: prime composite(2) factors product factor pairs prime factorization common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors REMEMBER: A product is the answer to a multiplication problem. Key Words: prime composite factors product factor pairs prime factorization common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors Definition: are numbers that are multiplied together to get a product. Key Words: prime composite(2) factors product factor pairs (prime factorization) common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors Definition: Factors are numbers that are multiplied together to get a product. Key Words: prime composite factors product factor pairs (prime factorization) common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors REMEMBER: Factor x Factor = Multiple or Product Example: (Factor) 7 x (Factor) 11 = (Product) 77

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Reasoning Mind Academy: Common Factors Definition: A number is a whole number that has only two factors: one and the number itself. Key Words: prime composite(2) factors product factor pairs (prime factorization) common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors Definition: A prime number is a whole number that has only two factors: one and the number itself. Key Words: prime composite factors product factor pairs (prime factorization) common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors Definition: A number is a whole number that has three or more factors. Key Words: prime composite(2) factors product factor pairs (prime factorization) common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors Definition: A composite number is a whole number that has three or more factors. Key Words: prime composite factors product factor pairs (prime factorization) common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors REMEMBER: numbers can be odd OR even. Key Words: prime composite(2) factor product factor pairs (prime factorization) common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors REMEMBER: Composite numbers can be odd OR even. Key Words: prime composite factor product factor pairs (prime factorization) common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors REMEMBER: is special! It is neither prime nor composite! Which Number????

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Reasoning Mind Academy: Common Factors REMEMBER: One is special! It is neither prime nor composite!

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Reasoning Mind Academy: Common Factors REMEMBER: are two numbers that, when multiplied, will always result in the same product, no matter the order of the numbers. Example: 2 x 4 = 8 or 4 x 2 = 8 Key Words: prime composite(2) factor product factor pairs prime factorization common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors REMEMBER: Factor pairs are two numbers that, when multiplied, will always result in the same product, no matter the order of the numbers. Example: 2 x 4 = 8 or 4 x 2 = 8 Key Words: prime composite factor product factor pairs prime factorization common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors Definition: A composite number written as the product of numbers is called the ______ of the number. Example: 2 x 2 x 3 = 12 Key Words: prime composite(2) factor product factor pairs prime factorization common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors Definition: A composite number written as the product of prime numbers is called the prime factorization of the number. Example: 2 x 2 x 3 = 12 Key Words: prime composite(2) factor product factor pairs prime factorization common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors REMEMBER: means to “factor”, “fracture”, or “break down” numbers. Key Words: prime composite(2) factor product factor pairs prime (factorization) common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors REMEMBER: Factorization means to “factor”, “fracture”, or “break down” numbers. Key Words: prime composite factor product factor pairs prime (factorization) common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors Definition: A is a number that is a factor of two or more given numbers. Example: 3 is a factor of both 33 and 24 Key Words: prime composite factor product factor pairs prime factorization common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors Definition: A common factor is a number that is a factor of two or more given numbers. Example: 3 is a factor of both 33 and 24 Key Words: prime composite factor product factor pairs prime factorization common factor Greatest Common Factor (GCF)

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Reasoning Mind Academy: Common Factors Definition: The (hint: GCF ) of two or more numbers is the greatest whole number that is a factor of each of the numbers. Key Words: prime composite factor product factor pairs prime factorization common factors Greatest Common Factor

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Reasoning Mind Academy: Common Factors Definition: The Greatest Common Factor (hint: GCF ) of two or more numbers is the greatest whole number that is a factor of each the numbers. Key Words: prime composite factor product factor pairs prime factorization common factors Greatest Common Factor

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Reasoning Mind Academy: Common Factors Example 1) Find all the factors of the number shown and classify them as prime or composite numbers. a.15 Step 1: Find ALL factor pairs that, when multiplied, will give a product of 15. Check numbers 1-10 as possible factors using (÷) if necessary

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Reasoning Mind Academy: Common Factors Example 1) Find all the factors of the number shown and classify them as prime or composite numbers. a.15 Step 1: Find ALL factor pairs that when multiplied will give a product of 15. Check numbers 1-10 as possible factors using division (÷) if necessary

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Reasoning Mind Academy: Common Factors Example 1) cont’d. a.15 Step 2: Decide if the number is prime or composite based on the number of factors listed. 15 has 4 factors, so it must be composite. Write: 15: 1, 3, 5, 15 COMPOSITE__

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Reasoning Mind Academy: Common Factors Example 1) cont’d: Find all the factors of the numbers below and classify them as prime or composite numbers. b) 17: ________________________ c) 48: _________________________ d) 57: __________________________

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Reasoning Mind Academy: Common Factors Example 1) cont’d: Find all the factors of the numbers below and classify them as prime or composite numbers. b) 17 : 1, 17, prime__________ c) 48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, composite d) 57 : 1, 57, prime__________

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Reasoning Mind Academy: Common Factors Example 2) Find the prime factorization of the number below using the factor tree method. a) Step 1: Draw the factor tree with the number at the top. Step 2: Use the prime cloud numbers to start factoring (ex. 2, 3, 5, 7, 11…) or start with a factor pair of the number. Step 3: Factor all composite numbers until you have all prime numbers circled. Step 4: Check your prime factorization using multiplication. Order the numbers from smallest to largest. Prime Factorization of 44: 2 x 2 x

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Reasoning Mind Academy: Common Factors Example 2) Find the prime factorization of the number below using the factor tree method. b) Prime Factors of 16: x x x

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Reasoning Mind Academy: Common Factors Example 2) Find the prime factorization of the number below using the factor tree method. b) Prime Factors of 16: 2 x 2 x 2 x 2

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Reasoning Mind Academy: Common Factors Example 2) Find the prime factorization of the number below using the factor tree method. b) Prime Factors of 42: x x

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Reasoning Mind Academy: Common Factors Example 2) Find the prime factorization of the number below using the factor tree method. b) Prime Factors of 42: 2 x 3 x 7

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Reasoning Mind Academy: Common Factors Example 3) Find all the common factors and the GCF of the numbers below. REMEMBER: The Greatest Common Factor is the BIGGEST factor the numbers both have! First, list all of the factors for each of the numbers. Factors of 20 ________________________ Factors of 24 _________________________

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Reasoning Mind Academy: Common Factors Example 3) Find all the common factors and the GCF of the numbers below. REMEMBER: The Greatest Common Factor is the BIGGEST factor the numbers both have! Factors of 20 __:_1, 2, 4, 5, 10, 20, Factors of 24 ____:__1, 2, 3, 4, 6, 8, 12, 24,

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Reasoning Mind Academy: Common Factors Draw a Venn Diagram.

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Reasoning Mind Academy: Common Factors Step 1: Write each number above the left or right circle of the Venn Diagram. Label “Common” for the shared space in the middle. 20 Common 24

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Reasoning Mind Academy: Common Factors Step 2: Factor both numbers. Find ALL factors for each number and write the factors in the Venn Diagram. Step 3: Circle all the factors that are the same on both circles in the Venn Diagram. Step 4: Write ALL of the common factors in the shared space in the middle. Step 5: Out of the common factors, identify the BIGGEST factor. Circle it and label as your GCF. 20 Common 24

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Reasoning Mind Academy: “Now, it’s your turn to try!” Independent Practice Problems Helpful Hints: Read the problem twice. Underline any important parts. Make a plan for solving the problem. Show your work, Do your best!

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