1. 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

2. 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

3. 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

4. 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

5. 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

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

7. 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)

8. 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)

9. 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)

10. 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)

11. 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)

12. 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)

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

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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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, COMPOSITE__

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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 _________________________

36. 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,

37. Reasoning Mind Academy: Common Factors
Draw a Venn Diagram.

38. 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. 
Common

39. 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.

40. 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.