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Greatest Common Factors

Greatest Common Factor Here We Come...... 6.NS.4 - Compute fluently with multi-digit numbers and find common factors and multiples

6.NS.4 - What will I do? Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Apply and extend previous understandings of numbers to the system of rational numbers.

Essential Question How do you find and use the greatest common factor of two whole numbers?

I Can Statements... I can determine if a number is prime or composite and explain why. I can find the prime factorization of a composite number. I can find all factors of any given number, less than or equal to 100.

I Can Statements... I can find the greatest common factor of any two numbers, less than or equal to 100. I can use the distributive property to rewrite a simple addition problem when the addends have a common factor.

First, I must know my divisibility rules. Do you? https://www.youtube.com/watch?v=RIRRJ88rASE

Next, I must know the difference between prime and composite. Do you? https://www.youtube.com/watch?v=AikMFJRQ7TY

Think about it… Student A says 51 is prime because it is odd. Student B says 51 is composite. Who do you agree with and Why?

A prime number is a number that can only be divided by only one and itself. A composite number is a number greater than one that is not prime. Prime or composite? 37 51 prime composite

Prime or Composite? 89 Prime Composite Both Neither

Factors are numbers that are multiplied 8 X 8 = 64

What does “Find the factors” mean? …find all the numbers you can multiply together to get that number as the product.

Always write factors from least to greatest. What are the factors of 27 Remember, you are being asked to find all the numbers that can be multiplied together to get the answer 27. 27: 1 X 27 3 X 9 1, 3, 9, 27 HINT: Always write factors from least to greatest.

Practice Find the factors: 1. 18 1, 2, 3, 6, 9, 18 2. 24 1, 2, 3, 4, 6, 8, 12, 24 3. 21 1, 3, 7, 21 4. 52 1, 2, 26, 52

Do Now: [In Math Binder] HAVE HOMEWORK ON DESK Do Now: [In Math Binder] Prime or Composite? Explain 1. 33 2. 73 3. 49 4. 6 Composite prime Composite Composite Find the Factors 5. 52 6. 60 -1, 2, 4, 13 26, 52 - 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Check Your Homework 16- 1, 2, 4, 8, 16 24- 1, 2, 3, 4, 6, 8, 12, 24 30- 1, 2, 3, 5, 6, 10, 15, 30 25- 1, 5, 25 36- 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors that two or more numbers have in common Common Factors What does COMMON mean? What does FACTORS mean? So….. COMMON FACTORS are: Factors that two or more numbers have in common

What are the common factors of 16 and 24? 24 1 X 24 2 X 12 3 X 8 4 X 6 16 1 X 16 2 X 8 4 X 4 Hint: Once you repeat a number you’re done!! 16: 1, 2, 4, 8, 16 24: 1, 2, 3, 4, 6, 8, 12, 24 Common Factors: 1, 2, 4, 8

Practice What are the common factors of: 6 & 9 24 & 48 25 & 45

Greatest Common Factor The greatest factor that both numbers have in common. GCF = Greatest Common Factor

Strategies to find GCF Backwards Method Prime factorization (Tree), T-chart, List or Rainbow Backwards Method Venn Diagram

Example of List Method GCF 60 and 96 60 -1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 96 – 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Rainbow Method

T-Chart Method List Factors for both numbers Circle common factors The highest number in common with be the GCF

Double T-Chart Method

Finding the GCF What is the GCF of 15 and 30? First: Find the factors of each whole number. 1 2 3 5 1 3 30 15 15 5 30 15 10 6

Finding the GCF Second: Circle all of the factors they have in common. 1 2 3 5 1 3 30 15 15 5 30 15 10 6

Finding the GCF Last: Determine the greatest number that both sets of factors have in common. 1 2 3 5 1 3 30 15 15 5 30 15 10 6 GCF is 15

Finding the GCF What is the GCF of 18 and 24? 1 2 3 4 1 2 3 24 18 18 9 6 24 12 8 6

Finding the GCF What is the GCF of 18 and 24? 1 2 3 4 1 2 3 24 18 18 9 6 24 12 8 6 GCF is 6

Prime factorization OR Write down the number they have in common only once, then write down the leftover numbers. Multiply them all together. OR Circle all the primes the 2 numbers have in common and multiply one set of them to get your GCF.

Prime Factorization Example

Step 3: Group the Greatest Factor 24 – 1,2,3,4,6,8,12,24 36 – 1,2,3,4,6,9,12,18,36 The GCF of 24 and 36 is… 12

Backwards Method

Think Backwards… Find Factors Circle Common Factors Group Greatest Factor

Find the GCF of 12 and 24 Step 1: Find the factors 12 – 1,2,3,4,6,12 24 – 1,2,3,4,6,8,12,24

Find the GCF of 12 and 24 Step 2:Circle the common factors 12 – 1,2,3,4,6,12 24 – 1,2,3,4,6,8,12,24

Find the GCF of 12 and 24 Step 3: Group the greatest factor 12 – 1,2,3,4,6,12 24 – 1,2,3,4,6,8,12,24 The GCF of 12 and 24 is… 12

Your turn! Find the Greatest Common Factor of 16 and 20. Remember…Find Factors, Circle Common, Group Greatest!

The Greatest Common Factor of 16 and 20 is… 4

Venn Diagram Method

Find the GCF 12 1 x 12 2 x 6 3 x 4 12: 1,2,3,4,6,12 9 1 x 9 3 x 3 9 : 1,3,9

Ticket out the Door Find the GCF: 12 & 26 9 & 21 Have Name on Paper Must include All factors listed Common Factors Circled GCF Written

Independent Practice List the factors: 36 18 27 List the common factors: 18, 22 52, 36 14, 9 List the factors: 36 18 27 List the GCF: 25, 40 30, 42

Copy Notes into your Composition notebook 9-25-17 9-25-17 Name Teacher/Class Period Title Date Anchor Chart Copy Notes into your Composition notebook Interim (Progress Report) goes home Tuesday! Must be Signed and Returned

Math Quiz and SLO Early Finishers: Login In using the following: Click on the LOCK ICON for Mastery Connect 1st SLO – 952020 2nd SLO – 101474 3rd SLO – 836653 4th SLO – 541743 6th SLO - 480232 Login In using the following: naumstudent green5 Early Finishers: Raise your hand to inform me… Choose an early finisher activity READ A BOOK, ABSOLUTELY NO TALKING

L e a s t C o m m o n M u l t I p l e

LCM Least Common Multiple 6.NS.4 Compute fluently with multi-digit numbers and find common factors and multiples

6.NS.4 - What will I do? Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Apply and extend previous understandings of numbers to the system of rational numbers.

How do you find and justify the least common multiple of two numbers? Essential Question How do you find and justify the least common multiple of two numbers?

I Can Statements… I can create a list of multiples for any number less than or equal to 12. I can find and justify the least common multiple of any two numbers, less than or equal to 12. https://www.youtube.com/watch?v=oYIHLUxzRr8

Poor George??? Importance of LCM How many packages of dogs and buns would George have to buy to have a bun for every dog?

The product you get when a number is multiplied by another number. What is ? Multiple The product you get when a number is multiplied by another number. Example: Multiples of 6 – 6, 12, 18, 24, 30,... (6 x 1) (6 x 2) (6 x 3) (6 x 4) (6 x 5) Multiples of 9 - 9, 18, 27, 36, 45,... (9 x 1) (9 x 2) (9 x 3) (9 x 4) (9 x 5)

LEAST COMMON MULTIPLE Smallest multiple they both have. Let’s put LEAST COMMON MULTIPLE in our own words Smallest multiple they both have. Example: LCM = 24 6 6, 12, 18, 24, 30, 36 8 8, 16, 24, 32, 40, 48

least common multiple (LCM): The smallest number that is a multiple of two or more numbers. least common denominator (LCD): The smallest number that is the multiple of two or more denominators.

Strategies to find LCM Backwards Method, The “L”adder Prime factorization (Tree), T-chart, Chart or List Backwards Method, The “L”adder

Let’s Practice!! 4 4, 8, 12, 16, 20, 24 LCM = 20 10 10, 20, 30, 40, 50, 60 12 12, 24, 36, 48, 60 LCM = 36 9 9, 18, 27, 36, 45

What if there are 3 numbers? Find the LCM of 4,6,and 8: 4 4, 8, 12, 16, 20, 24 6 6, 12, 18, 24, 30, 36 LCM = 24 8 8, 16, 24, 32, 40, 48

Write the first five multiples of each number. 1. 5 2. 6 3. 10 4. 12 5, 10, 15, 20, 25 6, 12, 18, 24, 30 10, 20, 30, 40, 50 12, 24, 36, 48, 60

Practice Find the first 10 multiples of 3 Is 40 a multiple of 8? Why? Is 63 a multiple of 5? Why?

Common Multiple A multiple with 2 or more numbers have in common. Example: Find the first 3 common multiples of 3 and 6. 3 3, 6, 9, 122, 15, 18… 6 6, 12, 18, ,24, 30, 36…

Practice No, 9 is not 2. 3 and 6 3. 4 and 12 4. 2 and 5 1. Is 42 a common multiple of 6 and 9? List 10 multiples of each number and circle the common multiples. 2. 3 and 6 3. 4 and 12 4. 2 and 5 No, 9 is not 3: 3, 6, 9, 12, 18, 21, 24, 27, 30 6: 6, 12, 18, 24, 30, 36, 42, 54, 60 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Least Common Multiple 6 6, 12, 18, 24, 30, 36… 8, 8 16, 24, 32, 40, The smallest multiple that 2 or more numbers have in common. LCM = Least Common Multiple Example: Find least common multiples of 6 and 8 6 6, 12, 18, 24, 30, 36… 8, 8 16, 24, 32, 40, 48…

Today, the school’s baseball and soccer teams have games Today, the school’s baseball and soccer teams have games. The baseball team plays every 7 days. The soccer team plays every 3 days. When will the teams have games on the same day again? 3,7 7: 7, 14, 21 , 28, 35, 42, . . . List multiples of 3 and 7. Find the smallest number that is in all the lists. 3: 3, 6, 9, 12, 15, 18, 21, . . . LCM: 21. In 21 days, both teams will have game on the same day again.

Independent Practice List the first 5 multiples of each number. 2 4 3. Name the LCM of the following numbers: 20 and 5 4. How many common multiples less than 50 do 8 and 9 have? Name them.

a board, eraser, and dry erase marker from the back Have homework on your desk turned to p11 9-26-17 Everyone should have: handout a board, eraser, and dry erase marker from the back Name Teacher/Period Title Date Write in your notes: GCF: Breaks numbers down; LCM; Multiplies (build numbers up) Do Now: Check for Understanding Find the least common multiple (LCM). 1. 6, 14 2. 9, 12 3. 5, 6, 10 4. 12, 16, 24, 36 5. Two students in Mrs. Stevens’ class are stacking blocks, one on top of the other. Cameron’s blocks are 4 cm high and Maddy’s blocks are 9 cm high. How tall will their stacks be when they are the same height for the first time? 42 36 30 144 36 cm

LCM Least Common Multiple 6.NS.4 Compute fluently with multi-digit numbers and find common factors and multiples

How do you find and justify the least common multiple of two numbers? Essential Question How do you find and justify the least common multiple of two numbers?

I Can Statements… I can create a list of multiples for any number less than or equal to 12. I can find and justify the least common multiple of any two numbers, less than or equal to 12.

Let’s Practice!! https://quizizz.com/admin/quiz/59b95ac2f85f8b11002b3135 https://quizizz.com/admin/quiz/57d8764602b75ab007653f59

ASSIGNMENT! Begin Handout from the back GRADED You can do it! Yeah! Try your best! You can do it!

Do Now: Check for Understanding Have homework on your desk 9-27-17 Everyone should have: handout Name Teacher/Period Title Date Write in your notes: GCF: Breaks numbers down; LCM; Multiplies (build numbers up) Do Now: Check for Understanding Ms. Madison directs two singing groups. One group has 28 students and the other has 36 students. For practice, she wants to divide each group into the greatest possible equal groups with no students left over. How many students will be in each group?    Two trains leave the train station at the same time. Train A stops every 8 minutes and Train B stops every 10 minutes. In how many minutes will they stop at the same time?   4 40 minutes

MAKE SURE YOU HAVE HANDOUT OUT OF THE BASKET (in the back) Math Review HAVE HOMEWORK ON DESK!!! (GRADED) MAKE SURE YOU HAVE HANDOUT OUT OF THE BASKET (in the back) GCF: Breaks numbers down; LCM: Multiplies (build numbers up) Early Finishers: Choose an early finisher activity READ A BOOK, ABSOLUTELY NO TALKING

Do Now: Check for Understanding Have homework on your desk 9-28-17 Name Teacher/Period Title Date Write in your notes: GCF: Breaks numbers down; LCM; Multiplies (build numbers up) Do Now: Check for Understanding Taylor is using two different colors of beads to make necklaces. She has 48 blue beads and 32 white beads. She wants to use the same number of blue and white on each necklace. What is the greatest number of necklaces she can make if she uses all of the beads?   Allison works at a bakery. She must box 30 rolls, 24 muffins, and 48biscuits so that all of the boxes have the same number of each. What isthe greatest number of boxes she can use?  16 6 boxes

MAKE SURE YOU HAVE QUIZ OUT OF THE BASKET (in the back) Login In using the following: naumstudent green5 Math Quiz TURN IN HOMEWORK IMMEDIATELY (GRADED) MAKE SURE YOU HAVE QUIZ OUT OF THE BASKET (in the back) Everyone Should Have a handout from the basket GCF: Breaks numbers down; LCM: Multiplies (build numbers up) Early Finishers: Get Computer to do Join.Quizizz.com Enter the 6-digit game code 583045 Choose an early finisher activity READ A BOOK, ABSOLUTELY NO TALKING

ASSIGNMENT! Finding the LCM Yeah! Try your best! You can do it!

24 50 36 60 72 105

Practice Time! Identify whether the following word problems could be solved using GCF or LCM…

Question #1 Mrs. Evans has 120 crayons and 30 pieces of paper to give to her students. What is the largest # of students she can have in her class so that each student gets equal # of crayons and equal # of paper.

GCF

Question #2 Rosa is making a game board that is 16 inches by 24 inches. She wants to use square tiles. What is the largest tile she can use?

GCF

Question #3 Z100 gave away a Z $100 bill for every 100th caller. Every 30th caller received free concert tickets. How many callers must get through before one of them receives both a coupon and a concert ticket?

LCM

Question #4 Two bikers are riding a circular path. The first rider completes a round in 12 minutes. The second rider completes a round in 18 minutes. If they both started at the same place and time and go in the same direction, after how many minutes will they meet again at the starting point?

LCM

Question #5 Solve the following: Sean has 8-inch pieces of toy train track and Ruth has 18-inch pieces of train track. How many of each piece would each child need to build tracks that are equal in length?

LCM 72 inch train track

Question #6 Solve the following: I am planting 50 apple trees and 30 peach trees. I want the same number and type of trees per row. What is the maximum number of trees I can plant per row?

(5 apple trees, and 3 peach trees per row) GCF 10 Rows (5 apple trees, and 3 peach trees per row)

Question # 7 Solve the following: Two faucets are dripping. One faucet will drip every 4 seconds and the other faucet drips every 9 seconds. If a drop of water falls from both faucets at the same, how many seconds will it be before you see the faucets drip at the same time again?

LCM Every 36 seconds

Question # 8 Solve the following: Three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of the same length. What is the greatest possible length of each plank ?

GCF 7 meters

QUIZ Answers… 1.) GCF 2.) GCF 3.) LCM 4.) LCM 5.) LCM – 72 inch train track 6.) GCF -10 Rows (5 apple trees, and 3 peach trees per row) 7) LCM – every 36 seconds 8) GCF – 7 m

Identify the prime numbers in the grid below(7) X X X 7 7 39 45 22 23 23 X X X X 63 17 17 9 57 81 X X X 11 11 77 27 19 19 99 X X X 69 2 2 49 37 37 1

Identify the prime numbers in the grid below.(7) X X X 127 127 129 153 303 313 313 X X X X 415 199 199 213 57 187 X X X 449 449 111 93 367 367 453 X X X 666 137 137 183 919 919 1

GCF and LCM Learning Objectives Know what factors and multiples are 23/05/2018 Level 5 GCF and LCM Learning Objectives Know what factors and multiples are Able to find the LCM of two numbers Able to find the GCF of two numbers

Lowest Common Multiple (LCM) Lowest Common Multiple – the lowest number in two or more numbers’ times tables.

Lowest Common Multiple (LCM) Q. Find the LCM of 4 and 6. Write out the first six numbers the 4 and 6 times tables Look for the first number that appears in both lists.

Lowest Common Multiple (LCM) Find the LCM of 4 and 6  4, 8, 12, 16, 20, 24,….  6, 12, 18, 24, 30, 36,… We want the LOWEST common multiple, so the LCM of 4 and 6 is… 12

Lowest Common Multiple (LCM) Find the LCM of 12 and 8.

Lowest Common Multiple (LCM) Find the LCM of the following: 2 and 5 3 and 4 4 and 8 5 and 6 24 10 e)3 and 8 4 and 9 8 and 10 4, 5 and 12 12 36 8 40 30 60

Greatest Common Factor (GCF) Greatest Common Factor (HCF) – the largest number that goes into two or more numbers exactly. Example: Find the HCF of 32 and 56 32  1, 2, 4, 8, 16, 32 56  1, 2, 4, 7, 8, 14, 28, 56 GCF = 8

Greatest Common Factor (GCF) Find the GCF of the following numbers: 4 e)32 and 80 f)60 and 10 g)36, 64, and 76 h)48, 60 and 84 a)8 and 12 b)9 and 15 c)10 and 30 d)18 and 33 16 3 12 10 4 3 12

Your turn… Find the GCF of the following: 18 and 28 16 and 40 42 and 90 40 and 63 20, 64 and 108 54, 90 and 162 Find the LCM of the following: 4 and 5 8 and 12 6 and 9 12 and 15 5, 8 and 10 4, 7 and 9 2 20 24 8 18 6 60 1 40 4 252 18

Do NOW Find the GCF of 30 and 54 Find the LCM of 9 and 12 Write factors of 48

GCF and LCM Learning Objectives: Level 5 23/05/2018 GCF and LCM Learning Objectives: Able to calculate the GCF and LCM of numbers using lists Able to write a number as a product of its prime factors Able to calculate the GCF and LCM of numbers using different strategies

Identify the prime numbers in the grid below. (7). X X X 7 7 39 45 22 23 23 X X X X 63 17 17 9 57 81 X X X 11 11 77 27 19 19 99 X X X 69 2 2 49 37 37 1

Identify the prime numbers in the grid below. (7) X X X 127 127 129 153 303 313 313 X X X X 415 199 199 213 57 187 X X X 449 449 111 93 367 367 453 X X X 666 137 137 183 919 919 1

Complete handout on GCF/LCM Assignment Complete handout on GCF/LCM