Lesson 6.2 Finding GCF of Two Whole Numbers

First, Let's study the divisibility Rules!

Multiple Choice

Is the number 87 divisible by 2?

• YES

• NO

Multiple Choice

Is the number 356 divisible by 2?

• YES

• NO

Multiple Choice

Is 702 divisible by 3

• Yes

• No

Multiple Select

Select which ones are divisible by 3

• 618

• 436

• 945

• 204

Multiple Choice

Is 202 divisible by 4?

• Yes

• No

Multiple Select

Select which ones are divisible by 4

• 616

• 310

• 436

• 714

Multiple Choice

Is 95 divisible by 5?

• Yes
• No

Multiple Choice

Is 1530 divisible by 5?

• Yes

• No

Multiple Choice

Is 846 divisible by 6?

• Yes

• No

Multiple Select

Select which numbers are divisible by 6

• 2,196

• 764

• 402

• 3,496

Multiple Choice

Is 63 divisible by 7. Show your work.

• Yes

• No

Multiple Choice

Which number is NOT divisible by 7?

• 49

• 324

• 91

• 77

• 147

Multiple Select

Choose ALL numbers that are divisible by 10

• 250

• 300

• 278

• 5

• 2,356,790

A number or variable that can be multiplied with another number or variable to produce the given term​

​

​What is a Factor?

Fill in the Blank

Find the missing factor.

81 = 9 x __

Fill in the Blank

Find the missing factor.

63 = 9 x __

Fill in the Blank

Find the missing factor.

56 = 7 x __

Multiple Choice

What is a factor?

• a factor is when you divide two numbers to get another number

• a number that multiplies with another number to get a product

• a factor the answer to a multiplication problem

• the same as a multiple

First there is the 'Listing Method'

• 16 = 1, 2, 4, 8, 16

• 24 = 1, 2, 3, 4, 6, 8, 12, 24

• If we will compare the list of factors of 16 and 24, we can identify the common factors.

• GCF is the highest common factor that appears on the list.

• The GCF of 16 and 24 is 8.

Multiple Choice

What is the Greatest Common Factor of 40 and 100?

• 20

• 10

• 5

• 1

Another way to find GCF is by the LADDER METHOD: I like to call it the CAKE METHOD.

Multiple Choice

What is the GCF of 15 and 20?

• 2

• 0

• 1

• 5

Multiple Choice

What is the GCF of 9 and 4?

• 0

• 1

• 3

• 5

Multiple Choice

What is the GCF of 56 and 80?

• 8

• 4

• 2

• 1

Multiple Choice

What is the GCF of 60 and 85?

• 1

• 7

• 12

• 5

Finding which prime factors multiply to create the actual number

​

Another way is called...
Prime Factorization

A diagram that shows all the factors of a given number​

​

Factor Tree

Find the Factors of each of the numbers given

Step 1:

30: 2 x 3 x 5

18: 2 x 3 x 3 ​

2 and 3 are the factors in common​

Example:

Highlight or Circle all the factors the two numbers have in common.

Step 2:

Some text here about the topic of discussion

Multiply the common factors to find the Greatest Common Factor of GCT

30: 2 x 3 x 5

18: 2 x 3 x 3 ​

​

GCF: 2 x 3 = 6​

Example:

Step 3

Some text here about the topic of discussion

Multiple Choice

Use a factor tree to find the prime factorization of 48

• 4x2x6
• 4x2²x3
• 3x2⁴
• 12x4

Multiple Choice

What is the GCF of 20 and 30, using a factor tree.

• 5
• 2
• 10
• 20

Lets try a word problem!

Linda has 20 forks and 16 knives to place in a silverware holders at the fast food restaurant where she works. She wants to distribute them equally with no forks or knives left over.

Open Ended

What is this problem about? I call it the gist.

2nd Read: Lets try a word problem!

Linda has 20 forks and 16 knives to place in a silverware holders at the fast food restaurant where she works. She wants to distribute them equally with no forks or knives left over. What is the greatest number of silverware holders Linda can stock?

Open Ended

What are they asking you to find?

Lets try a word problem!

Linda has 20 forks and 16 knives to place in a silverware holders at the fast food restaurant where she works. She wants to distribute them equally with no forks or knives left over. What is the greatest number of silverware holders Linda can stock?

Factors of 20: 1, 2, 4, 5, 10, 20

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

The greatest number of silverware holder Linda can stock is 4

Multiple Choice

Stanley is putting together first-aid kits. He has 20 large bandages and 15 small bandages, and he wants each kits to be identical, with no bandages left over. What is the greatest number of first-aid kits Stanley could put together?

• GCF: 4

• GCF: 5

• GCF: 6

• GCF: 7

Answer

Stanley is putting together first-aid kits. He has 20 large bandages and 15 small bandages, and he wants each kits to be identical, with no bandages left over. What is the greatest number of first-aid kits Stanley could put together?

Factor of 20: 1, 2, 4, 5, 10, 20

Factor of 15: 1, 3, 5, 15

The greatest number of first-aid kits Stanley can put together is 5.

Multiple Choice

The Lin Corporation would like to donate 4 computer and 6 printers to local schools. The corporation would like to make sure that each school receives the same set of computers and printers, with none left over. What is the greatest number of schools that the Lin Corporation can donate to?

• 2

• 6

• 4

• 1

Answer

The Lin Corporation would like to donate 4 computer and 6 printers to local schools. The corporation would like to make sure that each school receives the same set of computers and printers, with none left over. What is the greatest number of schools that the Lin Corporation can donate to?

4: 1, 2, 4

6: 1, 2, 3, 6

The greatest number of schools that the Lin Corporation can donate to is 2.

Fill in the Blank

Exit Ticket:

What is the GCF of 28 and 70

Fill in the Blank

My preferred method of solving for Greatest Common Factor is....