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Objective

Find the greatest common factor of two or more numbers

Vocabulary

Venn diagram

The use of circles to show how elements among sets of numbers or objects are related

Vocabulary

Greatest common factor (GCF)

The greatest of the common factors of two or more numbers

Review Vocabulary

Factor

Two or more numbers that are multiplied together to form a product

Review Vocabulary

Prime number

A whole number that has exactly two factors, 1 and the number itself

Example 1 Find the GCF by Listing Factors

Example 2 Find the GCF by Using Prime Factors

Example 3 Use the GCF to Solve a Problem

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Find the GCF of 36 and 48

To find the Greatest Common Factor (GCF)

You must prime factor the numbers

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36 48

Write the numbers

Put an upside down division sign with the numbers

Find the GCF of 36 and 48

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36

Prime factor 36

36 is an even number and the prime number 2 always goes into an even number

Place 2 outside the house

2

Divide 36 by 2

Put 18 below 36

18

Ask “is 18 a prime number?”

Find the GCF of 36 and 48

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362

18

Ask “is 18 a prime number?”

2 will go into 18 evenly

Put the prime factor bar on 18

Place 2 outside the bar

Divide 18 by 2

2

Place 9 under 18

Ask “is 9 a prime number?”

9

Find the GCF of 36 and 48

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362

182

Ask “is 9 a prime number?”

9

3 will go into 9 evenly and 3 is a prime number

Put the prime factor bar on 9

Place 3 outside the bar

3

Divide 9 by 3

Place 3 under 9

3

Find the GCF of 36 and 48

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362

182

Ask “is 3 a prime number?”

933

3 is a prime number so you are done prime factoring 36

Now prime factor 48

48

Ask “is 48 a prime number?”

2 will go into 48 because it is even

Place 2 outside the bar

2

Find the GCF of 36 and 48

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362

182

933

482

Divide 48 by 2

Place 24 under 48

24 Ask “is 24 a prime number?”

2 will go into 24 because it is even

Put the prime factor bar on 24

Place 2 outside the bar

2

Find the GCF of 36 and 48

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362

182

933

482

242

Divide 24 by 2

Place 12 under 24

Ask “is 12 a prime number?”

2 will go into 12 because it is even

Put the prime factor bar on 12

12

Place 2 outside the bar

2

Find the GCF of 36 and 48

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362

182

933

482

242

Divide 12 by 2

122

Place 6 under 12

6

Ask “is 6 a prime number?”

2 will go into 6 because it is even

Put the prime factor bar on 6

Place 2 outside the bar

2

Find the GCF of 36 and 48

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362

182

933

482

242

Divide 6 by 2

122

Place 3 under 6

623

Ask “is 3 a prime number?”

3 is a prime number so you are done prime factoring 48

Circle factors that are common in each number and write as factors

2 2 2 2 2 3 There are no more common factors

Find the GCF of 36 and 48

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362

182

933

482

242

Multiply the common factors122623

2 2 3

12

Identify the product as GCF

12 = GCFAnswer:

Find the GCF of 45 and 75

Answer: 15 = GCF

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Find the GCF of 52 and 78

Answer:

Prime factor both 52 and 78

52 782262

13

239313

Circle factors that are common in each number and write as factors

2 13

26

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= GCF

Multiply the common factorsIdentify the product as GCF

Find the GCF of 64 and 80 by using prime factors.

Answer: 16 = GCF

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SALES Annessa sold bags of cookies at a bake sale. She sold small, medium, and large bags, with a different number of cookies in each size bag. By the end of the sale, she used 18 cookies to fill the small bags, 27 cookies to fill the medium bags, and 45 cookies to fill the large bags. She sold the same number of bags for the three sizes. What is the greatest number of bags that she could have sold?

Find the factors of 18, 27, and 45

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Answer: The greatest number of bags she could have sold is 9 of each size

2718 45293

3

393

59333

Circle factors that are common in each number and write as factors

3 3= GCF9

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Multiply the common factors

Identify the product as GCF

CANDY Sarah is making bags of candy for a school fund-raiser. She is making three different sizes of bags. By the time Sarah had finished making the bags, she had used 24 lollipops to fill the small bags, 40 lollipops to fill the medium bags, and 64 lollipops to fill the large bags. She completed the same number of bags for the three sizes. What is the greatest number of bags she could have made?

Answer: 24 bags

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Assignment

Lesson 5:1 Greatest Common Factor 10 - 24 All