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### Factors and Multiples

### GCF Problem Solving

Prime and Composite numbers

August 27th Complete quiz on division of fractions.

Warm up: What do you remember about prime and composite numbers. Give an example of each. Complete WS on prime and composite numbers.

Number Theory GONE WILD!

Factors “Fit” into Families

Multiples Multiply like Rabbits!

What am I Learning Today?

Compute fluently with multi-digit numbers and find common factors and multiples.

How will I show that I learned it?

Through finding the greatest common factor of two whole numbers less than 100.

Vocabulary

Common factor: Factors shared by two or more whole numbers

Greatest Common Factor (GCF): The largest number that divides two or more numbers evenly.

What are common factors?

Factors shared by two or more whole numbers

Questions

Answers

What is the largest of the common factors?

The greatest common factor, or GCF.

How do I find the GCF?

Using the list method or the ladder

How do I use the list method?

1. List all the factor pairs for those two numbers.

2. Circle the largest factor that they share.

List the GCF for 28 and 42

Factors of 28:

Factors of 42:

1, 2, 4, 7, 14, 28

1, 2, 3, 6, 7, 14, 21, 42

The GCF of 28 and 42 is 14.

- Begin with a factor that divides into each number evenly. Does not have to be prime.
- Keep dividing until there are no more common factors.
- 3. Find the product of the numbers you divided by (GCF IS ON THE LEFT).

How do I use the ladder method?

Using the ladder, find the GCF for 40 and 16.

Questions

Answers

2

40 16

2• 2•2=

8

2

20 8

2

10 4

The GCF of 40 and 16 is 8

5 2

Find the Greatest Common Factor

Use BOTH the list and ladder method in order to check your answers.

Factors of 32: 1, 2, 4, 8, 16, 32

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

GCF of 32 and 24

32 24

2

16 12

2

8 6

2

4 3

GCF of 54 and 36

54 36

2

Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

27 18

3

9 6

3

3 2

Paired Discussion

Turn to a partner and discuss the following:

What is the GCF of two prime numbers? Explain.

Each prime number only has two factors, so they can ONLY share the number ONE.

How can you tell if a word problem requires you to use Greatest Common Factor?

If it is a GCF Problem

You are probably being asked:

Do we have to split things into smaller sections?

Are we trying to figure out how many people we can invite?

Are we trying to arrange something into rows or groups?

GCF Example: Applying what we have learned…

Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips?

- K: The pieces of cloth are 72 and 90 inches wide.
- W: How wide should she cut the strips so that they are the largest possible equal lengths.
- L: This problem can be solved using Greatest Common Factor because we are cutting or “dividing” the strips of cloth into smaller pieces (factor) of 72 and 90.

When is this useful?

Dr. Doyle’s band students have been invited to march in a parade along with another school. Since one band marches directly behind another, all the rows must have the same number of students. Dr. Doyle had 36 students and the other band has 60 students.

What is the greatest number

of students who can be in

each row?

12 students per row

Consumer Application

Peter has 18 oranges and 27 pears. He wants to make fruit baskets with the same number of each fruit in each basket. What is the greatest number of fruit baskets he can make?

HINT: The answer will be the greatest number of fruit baskets 18 oranges and 27 pears can form so that each basket has the same number of oranges, and each basket has the same number of pears.

The GCF of 18 and 27 is 9.

Question #1

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

GCF: 30 students

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: 8 inch tile

Question #3

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?

GCF: 10 trees

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