5 Minute Check Create a factor tree for the following on the back of your homework. Remember to circle the prime factors. 1. 20 2. 38 3. 99 4. 61.

5 Minute Check Create a factor tree for the following on the back of your homework. Remember to circle the prime factors. 1. 20 2. 38 3. 99 4. 61

5 Minute Check Create a factor tree for the following. Remember to circle the prime factors. 1. 20 20 / \ 2 x 10 I / \ 2 x 2 x 5

5 Minute Check Create a factor tree for the following. Remember to circle the prime factors. 2. 38

5 Minute Check Create a factor tree for the following. Remember to circle the prime factors. 2. 38 38 / \ 2 x 19

5 Minute Check Create a factor tree for the following. Remember to circle the prime factors. 3. 99 99 / \ 3 x 33 I / \ 3 x 3 x 11

5 Minute Check Create a factor tree for the following. Remember to circle the prime factors. 4. 61 61 is a prime number.

Lesson 6.1.1 Factors and Multiples
Friday, Aug 22 Lesson Factors and Multiples

Factors and Multiples Objective: To find the Greatest Common Factor and the Least Common Multiple.

Factors and Multiples A common factor is a number that is a factor of two or more numbers. The greatest of the common factors of two or more numbers is called the greatest common factor (GCF).

Factors and Multiples Greatest Common Factor – What does “greatest” mean?

Factors and Multiples Greatest Common Factor – What does “common” mean?

Factors and Multiples Greatest Common Factor – What does “factor” mean?

Factors and Multiples Greatest Common Factor would be the largest number that is in all factor rainbows of two or more numbers.

Factors and Multiples There are two ways to find the GCF -Factor List (Factor Rainbows) -Factor Trees

Factors and Multiples What is the GCF of 8 and 12?

Factors and Multiples What is the GCF of 8 and 12? Factor List Method Step 1 – List the factors (factor rainbow) for each number.

Factors and Multiples What is the GCF of 8 and 12? Factor List Method Step 1 – List the factors (factor rainbow) for each number. What is the factor list for 8?

Factors and Multiples What is the GCF of 8 and 12? Step 1 – List the factors (factor rainbow) for each number. 8:1, 2, 4, 8 What is the factor list for 12?

Factors and Multiples What is the GCF of 8 and 12? Step 1 – List the factors (factor rainbow) for each number. 8:1, 2, 4, 8 12:1,2,3,4,6,12

Factors and Multiples What is the GCF of 8 and 12? 8:1, 2, 4, 8 12:1,2,3,4,6,12 Step 2 – Circle the greatest number that is in all lists.

Factors and Multiples What is the GCF of 8 and 12? 8:1, 2, 4, 8 12:1,2,3,4,6,12 Step 2 – Circle the greatest number that is in all lists. The GCF of 8 and 12 is 4.

Factors and Multiples What is the GCF of 20 and 32? Do this on your own.

Factors and Multiples What is the GCF of 20 and 32? Step 1 – ?

Factors and Multiples What is the GCF of 20 and 32? Step 1 – List the factors (factor rainbow) for each number. 20: 1,2,4,5,10,20 32:1,2,4,8,16,32 Step 2 – ?

Factors and Multiples What is the GCF of 20 and 32? Step 1 – List the factors (factor rainbow) for each number. 20: 1,2,4,5,10,20 32:1,2,4,8,16,32 Step 2 – Circle the greatest number that is in all lists. The GCF of 20 and 32 is 4.

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row?

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with one slice of cake in each row?

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with one slice of cake in each row? Yes, we can have rows with one-slice of cake. But is it the greatest (largest) number of slices we can have in each row?

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with two slices of cake in each row?

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with two slices of cake in each row? No, if each row has to have an equal number of servings, how many “two slice rows” could we make with 15 red velvet slices?

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with three slices of cake in each row?

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with three slices of cake in each row? No, if each row has to have an equal number of servings, how many “three slice rows” could we make with 10 marble and 20 chocolate slices?

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with four slices of cake in each row?

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with four slices of cake in each row? No, if each row has to have an equal number of servings, how many “four slice rows” could we make with 10 marble and 15 red velvet slices?

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with five slices of cake in each row?

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Can we have rows with five slices of cake in each row? Yes, if each row has to have an equal number of servings, we would have 2 rows marble, 3 rows of red velvet slices and 4 rows of chocolate.

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Is there an easier way to do this?

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? Is there an easier way to do this? Yes, we can find the GCF of 10, 15 and 20.

Factors and Multiples There are one-slice servings of three types of cake on a table. Each row has an equal number of servings and only one type of cake. What is the greatest number of servings in each row? 10; 1, 2, 5, 10 15; 1, 3, 5, 15 20 ; 1, 2, 4, 5, 10, 20 The greatest number of servings in each row (GCF) would be 5.

Factors and Multiples Lana earned $49 on Friday, $42 on Saturday, and $21 on Sunday selling bracelets. She sold each bracelet for the same amount. What is the most she could have charged for each bracelet? Do this on your own.

Factors and Multiples Lana earned $49 on Friday, $42 on Saturday, and $21 on Sunday selling bracelets. She sold each bracelet for the same amount. What is the most she could have charged for each bracelet? 49: 1, 7, 49 42: 1, 2, 6, 7, 21, 42 21: 1, 3, 7, 21 The most she could have charged for each bracelet was $7.

Factors and Multiples Lana earned $49 on Friday, $42 on Saturday, and $21 on Sunday selling bracelets. She sold each bracelet for the same amount. What is the most she could have charged for each bracelet? If she sold them for $7, how many did she sell on Friday?

Factors and Multiples Lana earned $49 on Friday, $42 on Saturday, and $21 on Sunday selling bracelets. She sold each bracelet for the same amount. What is the most she could have charged for each bracelet? If she sold them for $7, how many did she sell on Friday? $49 ÷ $7 = 7 bracelets

Factors and Multiples We can also find the GCF with factor trees.

Factors and Multiples What is the GCF of 8 and 12?

Factors and Multiples What is the GCF of 8 and 12? Factor Tree Method Step 1 – Create a factor tree for each number / \ / \ 2 x 4 2 x 6 I / \ I / \ 2 x 2 x 2 2 x 2 x 3 Write this down

Factors and Multiples What is the GCF of 8 and 12? 8 12 / \ / \ 2 x 4 2 x 6 I / \ I / \ 2 x 2 x 2 2 x 2 x 3 Step 2 – Make a Venn Diagram with the prime factors.

8 12 Factors and Multiples What is the GCF of 8 and 12?
8 = 2 x 2 x = 2 x 2 x 3 What factors are common? Write this down

8 = 2 x 2 x = 2 x 2 x 3 What factors are common? 2

8 = 2 x 2 x = 2 x 2 x 3 What factors remain? 2

Factors and Multiples What is the GCF of 8 and 12? 8 = 2 x 2 x 2 12 = 2 x 2 x 3 What factors remain?

Factors and Multiples What is the GCF of 8 and 12? Step 3 – Multiply the numbers in the intersection

Factors and Multiples What is the GCF of 8 and 12? Step 3 – Multiply the numbers in the intersection . The GCF is 4 ( 2 x 2)

Factors and Multiples Since the factor tree method is longer and more difficult, in what situations would you choose to use this method, rather than the factor list method?

Factors and Multiples Since the factor tree method is longer, in what situations would you choose to use this method, rather than the factor list method? If the number is larger and has a long factor list.

Factors and Multiples Before you try either method, try and use Mr. Avery’s GCF rule. Mr. Avery’s GCF Rule – If the smaller number goes into the larger number(s), the smaller number is the GCF.

Factors and Multiples What is the GCF of 18 and 30. Do this on your own.

Factors and Multiples What is the GCF of 18 and ; 1, 2, 3, 6, 9, 18 30; 1, 2, 3, 5, 6, 10, 15, 30 The GCF of 18 and 30 is 6.

Factors and Multiples What is the GCF of 6 and 12? Do this on your own.

Factors and Multiples What is the GCF of 6 and 12? Mr. Avery’s Rule - Since 6 x 2 = 12 6 is the GCF. You can prove this by factor lists. 6; 1, 2,3, 6 12; 1, 2, 3, 4, 6, 12

Factors and Multiples What is the GCF of 32 and ; 1, 2, 4, 8, 16, 32 48; 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 The GCF of 32 and 48 is 16.

Factors and Multiples What is the GCF of 22 and 66. Mr. Avery’s Rule - Since 22 x 3 = is the GCF.

Factors and Multiples What is the GCF of any two prime numbers?

Factors and Multiples What is the GCF of any two prime numbers? Since prime numbers have a factor list of 1 and itself, the GCF would be 1. Example – 43; 1, 43 31; 1, 31

Factors and Multiples The least number that is a multiple of two or more whole numbers is the least common multiple (LCM) of the numbers.

Factors and Multiples Least Common Multiple– What does “least” mean?

Factors and Multiples Least Common Multiple– What does “common” mean?

Factors and Multiples Least Common Multiple– What does “multiple” mean?

Factors and Multiples Least Common Multiple would be the smallest number that is in all multiple lists.

Factors and Multiples There are two ways to find the LCM. -Multiples List -Factor Trees

Factors and Multiples Find the LCM of 2 and 3.

Factors and Multiples Find the LCM of 2 and 3. Multiples List Method Step 1 – List the multiples (multiples list)for each number. What is the multiples list of 2?

Factors and Multiples Find the LCM of 2 and 3. Step 1 – List the multiples (multiples list)for each number. 2; 2, 4, 6, 8, 10….. What is the multiples list of 3?

Factors and Multiples Find the LCM of 2 and 3. Step 1 – List the multiples for each number. (Create a multiples list) 2; 2, 4, 6, 8, 10….. 3; 3, 6, 9, 12, 15…..

Factors and Multiples Find the LCM of 2 and 3. 2; 2, 4, 6, 8, 10….. 3; 3, 6, 9, 12, 15….. Step 2 – Circle the smallest number that is in all lists.

Factors and Multiples Find the LCM of 2 and 3. 2; 2, 4, 6, 8, 10….. 3; 3, 6, 9, 12, 15….. Step 2 – Circle the smallest number that is in all lists. The LCM of 2 and 3 is 6.

Factors and Multiples Find the LCM of 2 and 6. Step 1 ?

Factors and Multiples Find the LCM of 2 and 6. Step 1 – List the multiples (multiples list)for each number. 2; 2, 4, 6, 8, 10….. 6; 6, 12, 18, 24….. Step 2?

Factors and Multiples Find the LCM of 2 and 6. Step 1 – List the multiples (multiples list)for each number. 2; 2, 4, 6, 8, 10….. 6; 6, 12, 18, 24….. Step 2 – Circle the smallest number that is in all lists. The LCM of 2 and 6 is 6.

Factors and Multiples Mr. Avery’s LCM Rule – If the smaller number goes into the larger number(s), the larger number is the LCM. Since 2 x 3 = 6, the LCM of 2 and 6 is 6. .

Factors and Multiples Find the LCM of 4, 5 and 10. Do this on your own.

Factors and Multiples Find the LCM of 4, 5 and 10. 4; 4, 8, 12, 16, 20 , 24…. 5; 5, 10, 15, 20, 25….. 10; 10, 20, 30 …… The LCM of 4, 5, and 10 is 20.

Factors and Multiples Find the LCM of 12 and 15. Factor Tree Method

Factors and Multiples Find the LCM of 12 and 15. Factor Tree Method Step 1 – Create a factor tree for each number / \ / \ 2 x 6 3 x 5 I / \ 2 x 2 x 3 Write this down.

Factors and Multiples Find the LCM of 12 and / \ / \ 2 x 6 3 x 5 I / \ 2 x 2 x 3 Step 2 – Make a Venn Diagram with the prime factors.

12 15 Factors and Multiples Find the LCM of 12 and 15.
12 = 2 x 2 x = 3 x 5 What factors are common?

12 = 2 x 2 x = 3 x 5 What factors are common? 3

12 = 2 x 2 x = 3 x 5 What factors remain? 3

12 5 15 Factors and Multiples Find the LCM of 12 and 15.
12 = 2 x 2 x = 3 x 5 What factors remain? 2

12 5 15 Step 3 – Multiply ALL the numbers inside the Venn Diagram.
Factors and Multiples Find the LCM of 12 and 15. Step 3 – Multiply ALL the numbers inside the Venn Diagram. 2

12 5 15 The LCM is 60 (2 x2x3x5) Factors and Multiples
Find the LCM of 12 and 15. The LCM is 60 (2 x2x3x5) 2

Factors and Multiples Find the LCM of 3, 5 and 7. (Do this on your own)

Factors and Multiples Find the LCM of 3, 5 and 7. 3; 3, 6, 9, 12, 15, 18, ….. 5; 5, 10, 15, 20, …… 7; 7, 14, 21, 28, 35, ……

Factors and Multiples Find the LCM of 3, 5 and 7. Mr. Avery’s Second LCM Rule – If all the numbers are prime, the LCM is the product of those numbers. Since 3, 5, and 7 are prime, the LCM is the product. The LCM is 105 (3 x 5 x 7)

Factors and Multiples Find the LCM of 9, 12 and 18. 9; 9, 18, 27, 36, 45, 54…… 12; 12, 24, 36, 48…… 18; 18, 36, 54, 72…… The LCM of 9, 12, and 18 is 36.

Factors and Multiples Find the LCM of 5, 10 and 15. 5; 5, 10, 15, 25, 30, 35, 40…… 10; 10, 20, 30, 40…… 15; 15, 30, 45, 60…… The LCM of 5, 10, and 15 is 30.

Factors and Multiples Ernesto has painting class every 2 weeks. Kamala has pottery class every 5 weeks. Ernesto and Kamala met at the art building for class this week. How many weeks will it be before they see each other again? (Do this on your own)

Factors and Multiples Ernesto has painting class every 2 weeks. Kamala has pottery class every 5 weeks. Ernesto and Kamala met at the art building for class this week. How many weeks will it be before they see each other again? 2; 2, 4, 6, 8, 10, 12, 14……. 5; 5, 10, 15, 20……. They will see each other again in 10 weeks.

OAA Review At Stone Middle School, the band has a concert every 4 weeks and the drama club has a play every 6 weeks. Both groups performed during the first week of school. When is the next time they will perform in the same week? (Do this on your own)

OAA Review At Stone Middle School, the band has a concert every 4 weeks and the drama club has a play every 6 weeks. Both groups performed during the first week of school. When is the next time they will perform in the same week? 4; 4, 8, 12, 16, 20, 24, 28….. 6; 6, 12, 18, 24, 30, 36……… They will perform together again the 12th week of school.

OAA Review Buses to the stadium leave Central Station every 10 minutes. Buses to the zoo leave Central Station every 16 minutes. Both buses leave Central Station at 4PM. When is the next time both buses will leave at the same time? (Do this on your own)

OAA Review Buses to the stadium leave Central Station every 10 minutes. Buses to the zoo leave Central Station every 16 minutes. Both buses leave Central Station at 4PM. When is the next time both buses will leave at the same time? 10; 10, 20, 30, 40, 50, 60, 70, 80, 90, 100….. 16; 16, 32, 48, 64, 80, 96……… They will leave at the same time 80 minutes later, which is 5:20PM.

OAA Review Ms. Mason is packaging science supplies for a group of students. She has 40 hand lenses, 32 pairs of tweezers, and 28 pens. She want to package the supplies so that every group has the same number of each item. What is the greatest number of packages she can make without having leftover items? (Do this on your own)

OAA Review Ms. Mason is packaging science supplies for a group of students. She has 40 hand lenses, 32 pairs of tweezers, and 28 pens. She want to package the supplies so that every group has the same number of each item. What is the greatest number of packages she can make without having leftover items? 40; 1, 2, 4, 5, 8, 10, 20, 40 32; 1, 2, 4, 8, 16, 32 28; 1, 2, 4, 7, 14, 28

OAA Review Ms. Mason is packaging science supplies for a group of students. She has 40 hand lenses, 32 pairs of tweezers, and 28 pens. She want to package the supplies so that every group has the same number of each item. What is the greatest number of packages she can make without having leftover items? / \ / \ / \ 2 x x x I / \ I / \ I / \ 2 x x x x x x 7 I I / \ 2 x 2 x 2 x 4 I I I / \ 2 x 2 x 2 x 2 x 2

OAA Review Ms. Mason is packaging science supplies for a group of students. She has 40 hand lenses, 32 pairs of tweezers, and 28 pens. She want to package the supplies so that every group has the same number of each item. What is the greatest number of packages she can make without having leftover items? To find the GCF we multiply the numbers in the intersection. 2 x 2 =

Factors and Multiples Agenda Notes Homework – Homework Practice Due Monday, Aug 25 Accumulative Review 1 Due Sept 4

5 Minute Check Create a factor tree for the following on the back of your homework. Remember to circle the prime factors. 1. 20 2. 38 3. 99 4. 61.

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5 Minute Check Create a factor tree for the following on the back of your homework. Remember to circle the prime factors. 1. 20 2. 38 3. 99 4. 61.

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Presentation on theme: "5 Minute Check Create a factor tree for the following on the back of your homework. Remember to circle the prime factors. 1. 20 2. 38 3. 99 4. 61."— Presentation transcript:

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