Common Factors *Identify Common Factors of a Set of Whole Numbers 5.3D 5.3D Identify Common Factors of a Set of Whole Numbers & 5.5B Identify Prime & Composite Numbers using Patterns in Factor Pairs- Supporting Standards Suggested method: - Use students RM Notebooks to log any guided theory or problems taught in offline lessons to show consistency in the RM Online classroom and Offline Lessons. Feel free to modify in order to best serve your students needs. *Identify Common Factors of a Set of Whole Numbers 5.3D *Identify Prime & Composite Numbers using Patterns in Factor Pairs 5.5B

REMEMBER: A is the answer to a multiplication problem. 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) Answer: product

REMEMBER: A product is the answer to a multiplication problem. 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) Answer: product

Definition: are numbers that are multiplied together to get a product. 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) Answer: factors

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) Answer: factors

Reasoning Mind Academy: Common Factors REMEMBER: Factor x Factor = Multiple or Product  Example: (Factor) 7 x (Factor) 11 = (Product) 77 Write in Notebook.

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) Answer: prime (Examples: 5, 13, 37, 53)

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) Answer: prime (Examples: 5, 13, 37, 53)

Definition: A number is a whole number that has three or more factors. 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) Answer: composite (Examples: 9, 18, 36, 100)

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) Answer: composite (Examples: 9, 18, 36, 100)

REMEMBER: numbers can be odd OR even. 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) Answer: composite (Examples: 8, 12, 15, 39)

REMEMBER: Composite numbers can be odd OR even. 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) Answer: composite (Examples: 8, 12, 15, 39)

Reasoning Mind Academy: Common Factors REMEMBER: is special! It is neither prime nor composite!  Which Number???? Answer: 1

Reasoning Mind Academy: Common Factors REMEMBER: One is special! It is neither prime nor composite!  Answer: 1

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) Answer: Factor Pairs

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) Answer: Factor Pairs

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) Answer: prime, prime factorization

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) Answer: prime, prime factorization

REMEMBER: means to “factor”, “fracture”, or “break down” numbers. 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) Answer: factorization

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) Answer: factorization

Example: 3 is a factor of both 33 and 24 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) Answer: common factor

Example: 3 is a factor of both 33 and 24 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) Answer: common factor

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 Answer: Greatest Common Factor

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 Answer: Greatest Common Factor

Reasoning Mind Academy: Common Factors Example 1) Find all the factors of the number shown and classify them as prime or composite numbers. 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. Answer: Division 1 15 3 5

Reasoning Mind Academy: Common Factors Example 1) Find all the factors of the number shown and classify them as prime or composite numbers. 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. Answer: Division 1 15 3 5

Reasoning Mind Academy: Common Factors Example 1) cont’d. 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__

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: __________________________ Answer: b) 17: 1, 17, prime c) 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, composite d) 57: 1, 57, prime

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__________ Answer: b) 17: 1, 17, prime c) 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, composite d) 57: 1, 57, prime

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. 11 4 Answer: 2, 2, 11 2 2 Prime Factorization of 44: 2 x 2 x 11

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

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

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

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

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 _________________________

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,

Reasoning Mind Academy: Common Factors Draw a Venn Diagram.  

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

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.

Independent Practice Problems 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! Print off practice problems from lessons. Feel free to add any incentives or extra goals for student achievement in offline lessons.