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 n Lesson 1: What are prime and composite n n 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?

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

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

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

Divisibility Rules Table of Contents n To quickly tell if a number is prime or composite use the following rules: n A number is divisible by: n n n n 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! EQ: What are prime and composite numbers?

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

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

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

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

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

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

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

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

Factor Tree Table of Contents n Steps to find Prime Factorization: n n n 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 EQ: How is the prime factorization of a number determined?

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

Table of Contents Examples n 2. Find the prime factorization of 255. n Draw a factor tree 255 n n n Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: 5 51 3 17 3 x 5 x 17 No need for exponents EQ: How is the prime factorization of a number determined?

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

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

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

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

Table of Contents To Find GCF n Make a t-chart n List all of the factors of each number n Find the factors that are the same n Circle the largest of the common factors n 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 EQ: How is the greatest common factor of two or more numbers found?

Examples Table of Contents n 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. EQ: How is the greatest common factor of two or more numbers found?

Examples Table of Contents n 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 EQ: How is the greatest common factor of two or more numbers found?

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

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

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

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

Table of Contents To Find LCM n Make a t-chart n List the first few multiples of each number n Circle the first multiple they have in common n 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. EQ: How is the least common multiple of two or more numbers found?

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

Examples Table of Contents n 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. EQ: How is the least common multiple of two or more numbers found?

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

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

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