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Greatest Common Factor Least Common Multiple Prime Factorization

Greatest Common Factor Least Common Multiple Prime Factorization. 6 th Grade Mathematics Miss Quimby’s Class. Table of Contents. Lesson 1: What are prime and composite numbers? Lesson 2: How is the prime factorization of a number determined?

Greatest Common Factor Least Common Multiple Prime Factorization

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1. Greatest Common FactorLeast Common MultiplePrime Factorization 6th Grade Mathematics Miss Quimby’s Class

2. Table of Contents • Lesson 1: What are prime and composite numbers? • Lesson 2: How is the prime factorization of a number determined? • Lesson 3: How is the greatest common factor of two or more numbers found? • Lesson 4: How is the least common multiple of two or more numbers found? • Lesson 5: How is upside-down division used to find prime factorization, GCF, and LCM?

3. What do these three pictures have in common? Table of Contents The are all prime!

4. Key Vocabulary Page • On the top of the next clean page write: • GCF/LCM/Prime Factorization Vocabulary • Create a word column and a definition column • Paperclip the next 2 pages together. • Keep track of all new vocabulary on these pages. • At the end of the unit you will have a key vocabulary list to use to study. Table of Contents

5. With no remainder Key Vocabulary • Prime Number: Any whole number, greater than 1, that can only be divided evenly by 1 and itself. • Example: • 3 can only be divided by 3 and 1. • 3 ÷ 3 = 1 • 3 ÷ 1 = 3 • Composite Number: Any whole number, greater than 1, that can be divided evenly by a number other than 1 or itself. • Example: • 4 can be divided by 4, 1, and 2 • 4 ÷ 4 = 1 • 4 ÷ 1 = 4 • 4 ÷ 2 = 2 Table of Contents EQ: What are prime and composite numbers?

6. Divisibility Rules • To quickly tell if a number is prime or composite use the following rules: • A number is divisible by: • 2 if the ones digit is divisible by 2 • 3 if the sum of the digits is divisible by 3 • 5 if the ones digit is 0 or 5 • 6 if the number is divisible by both 2 and 3 • 9 if the sum of the digits is divisible by 9 • 10 if the ones digit is 0. • Keep in mind that some numbers do NOT have rules! Table of Contents EQ: What are prime and composite numbers?

7. Examples • 1. Is 46 divisible by 2? • The ones digit is 6. • Since 6 ÷ 2 = 3, 46 is divisible by 2. • 2. Is 428 divisible by 3? • The sum of the digits is 4 + 2 + 8 = 14. • Since 14 is not divisible by 3, 428 is not divisible by 3. • 3. Is 2,736 divisible by 9? • The sum of the digits is 2 + 7 + 3 + 6 = 18. • Since 18 ÷ 9 = 2, 2,736 is divisible by 9. Table of Contents EQ: What are prime and composite numbers?

8. Prime vs. Composite • Every number is either prime or composite. • Use the divisibility rules • Ask yourself, “Is there anything that can divide evenly into this number other than itself and 1?” • Yes- composite. • No- prime. • ODD does NOT equal Prime! Table of Contents EQ: What are prime and composite numbers?

9. Examples • 1. Is 18 a prime or composite number? • Does anything other than 1 and 18 divide evenly into 18? • Yes, 2, 3, 6, and 9. • So, 18 is composite. • 2. Is 29 a prime or composite number? • Does anything other than 1 and 29 divide evenly into 29? • No, only 1 and 29. • So, 29 is prime. Table of Contents EQ: What are prime and composite numbers?

10. Practice • Follow along as we complete the Buckle Down Book Prime and Composite Numbers worksheet. Table of Contents EQ: What are prime and composite numbers?

11. Classwork • Complete the IIII Minutes to IV Minutes packet on prime and composite numbers. • I will be collecting this for a grade. • If you need help with any part of this packet, please see me ASAP. Table of Contents EQ: What are prime and composite numbers?

12. How will you remember? • How will you remember the difference between a prime number and a composite number? • Write your idea on a sticky note. • Be sure to put your name on it! • Stick your idea to the door before you leave! Table of Contents EQ: What are prime and composite numbers?

13. How do you change a composite number to a prime number? • What are your ideas? Table of Contents EQ: How is the prime factorization of a number determined?

14. To multiply Re-writing Key Vocabulary • Prime Factorization: Expressing a composite number as the product of prime numbers. • Example: • the prime factorization of 63 is 3 x 3 x 7= 32 x 7. Table of Contents EQ: How is the prime factorization of a number determined?

15. Factor Tree • Steps to find Prime Factorization: • Step 1: Write the composite number. • Step 2: Find two numbers whose product is the composite and write them directly below. • Step 3: Circle any prime numbers. • Step 4: repeat steps 2-3 for the new composite numbers. • Step 5: Write all prime numbers as a product in order from least to greatest. • Step 6: Re-write using exponents Table of Contents EQ: How is the prime factorization of a number determined?

16. Examples • 1. Find the prime factorization of 36. • Draw a factor tree • Step1: • Step 2: • Step 3: • Step 4: • Step 5: • Step 6: 36 4 9 2 2 3 3 2 x 2 x 3 x 3 22 x 32 No primes Table of Contents EQ: How is the prime factorization of a number determined?

17. Examples • 2. Find the prime factorization of 255. • Draw a factor tree • Step1: • Step 2: • Step 3: • Step 4: • Step 5: • Step 6: 255 5 51 3 17 3 x 5 x 17 Table of Contents No need for exponents EQ: How is the prime factorization of a number determined?

18. Practice • Follow along as we complete the Buckle Down Book Prime Factorization worksheet. Table of Contents EQ: What are prime and composite numbers?

19. Classwork • Complete the Prime factorization worksheet • I will be collecting this for a grade. • If you need help with any part of this paper, please see me ASAP. Table of Contents EQ: What are prime and composite numbers?

20. Solve the following problem • Use a strategy: Draw a picture • Is there an easier way to solve the problem? • Yes, use the factor of 27 and 45! Table of Contents EQ: How is the greatest common factor of two or more numbers found?

21. Number that divides evenly biggest same Key Vocabulary • Factor: A number that divides into a whole number evenly. • Example: • 5 is a factor of 30. • Greatest Common Factor (GCF): The greatest of the common factors of two or more numbers. • Example: • The GCF of 24 and 30 is 6. Table of Contents EQ: How is the greatest common factor of two or more numbers found?

22. To Find GCF • Make a t-chart • List all of the factors of each number • Find the factors that are the same • Circle the largest of the common factors • There will always be a GCF • it may be 1 • Example: GCF of 2 and 3 is 1. • it may be the smallest number • Example: GCF of 4 and 8 is 4. • It will never be bigger than the largest number Table of Contents EQ: How is the greatest common factor of two or more numbers found?

23. Examples • 1. Find the GCF of 27 and 45 27: 1, 3, 9, 27 45: 1, 3, 5, 9, 15, 45 • Common Factors: 1, 3, 9 • GCF: 9 • Therefore, the greatest number of flag line and drill team members in each row is 9. Table of Contents EQ: How is the greatest common factor of two or more numbers found?

24. Examples • 2. Find the GCF of 32, 48 and 80 32: 1, 2, 4, 8, 16, 32 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 80: 1, 2, 4, 5, 8, 10, 16, 20, 40,80 • Common Factors: 1, 2, 4, 8, 16 • GCF: 16 Table of Contents EQ: How is the greatest common factor of two or more numbers found?

25. Practice • Follow along as we complete the Buckle Down Book Greatest Common Factor worksheet. Table of Contents EQ: What are prime and composite numbers?

26. Ticket out The Door • On your index card • 1. Explain how to find the GCF of 12 and 18. • 2. Tell how the GCF of two numbers should be one of the two numbers. Table of Contents EQ: How is the greatest common factor of two or more numbers found?

27. Solve the Problem • Is there an easier way to solve this problem? • Yes! Find the multiples! Table of Contents EQ: How is the least common multiple of two or more numbers found?

28. multiply smallest product same Key Vocabulary • Multiple: The product of the number and any whole number. • Example: • A multiple of 4 is 24. • Least Common Multiple (LCM): The least of the common multiples of two or more numbers. • Example: • The LCM of 2 and 3 is 6. Table of Contents EQ: How is the least common multiple of two or more numbers found?

29. To Find LCM • Make a t-chart • List the first few multiples of each number • Circle the first multiple they have in common • There will always be an LCM • It may be the product of the two numbers, but never bigger than the product • Example: The LCM of 5 and 8 is 40 • It may be the larger number • Example: The LCM of 4 and 8 is 8 • It will never be smaller than the smaller number. Table of Contents EQ: How is the least common multiple of two or more numbers found?

30. Examples • 1. Find the LCM of 4 and 7 4: 4, 8, 12, 16, 20, 24, 28 7: 7, 14, 21, 28 • LCM: 28 Table of Contents EQ: How is the least common multiple of two or more numbers found?

31. Examples • 2. Find the LCM of 10, 16, and 8. 10: 10, 20, 30, 40, 50, 60, 70, 80 16: 16, 32, 64, 80 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 • LCM: 80 • So, the least amount of packages Joe needs to buy to have the same amount of cups, napkins, and plates is 8 packages of plates, 5 packages of napkins, and 10 packages of cups. Table of Contents EQ: How is the least common multiple of two or more numbers found?

32. Practice • Follow along as we complete the Buckle Down Book Least Common Multiple worksheet. Table of Contents EQ: How is the least common multiple of two or more numbers found?

33. Write a letter • Write a letter to an absent student explaining how to find the LCM of two or more numbers. • Be sure to include an example as well as a written explanation of the steps you used to find LCM. Table of Contents EQ: How is the least common multiple of two or more numbers found?

34. Key Vocabulary • Upside-Down Division: A strategy to find the prime factorization, GCF, and LCM of two or more numbers using division.

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