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# Greatest Common Factor - PowerPoint PPT Presentation

Greatest Common Factor. GCF. Divisibility Rules. 2 , if it ends in a even number in the ones place ( 0,2,4,6,8 ). Example: 55 8 because there is a 8 in the ones place 3 , if the sum of its digits is divisible by 3. Example: 81 because 8 + 1 = 9 and 9 is divisible by 3

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## PowerPoint Slideshow about ' Greatest Common Factor' - sylvester-stewart

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### Greatest Common Factor

GCF

• 2, if it ends in a even number in the ones place (0,2,4,6,8).

• Example: 558because there is a 8 in the ones place

• 3, if the sum of its digits is divisible by 3.

• Example: 81because 8 + 1 = 9 and 9 is divisible by 3

• 4, if the last 2 digits are divisible by 4

• Example: 124because 24 is divisible by 4

• 5, if the ones digit is 5 or 0.

• Example: 1125because there is a 5 in the ones place

• 6, if the number is divisible by both 2 and 3

• Example: 48

• There is an 8 in the ones place so it is divisible by 2

• 8 + 4 = 12 and 12 is divisible by 3

• 8, if the last 3 digits are divisible by 8

• Example: 1240because 240 is divisible by 8

• 9, if the sum of the digits is divisible by 9

• Example: 468because 4 + 6 + 8 = 18 and 18 is divisible by 9

• 10, if the number ends in a zero

• Example: 50because the number ends in zero

• DEFINITION: Any integer that can evenly divide into all the numbers in a given set of numbers

• Example: Find the common factors of 10 and 20 by listing all the factors.

• Factors of 10: _____________________________

• Factors of 20: _____________________________

• Common Factors of 10 and 20: ______________________

1, 2, 5, 10

1, 2, 4, 5, 10, 20

1, 2, 5, 10

• DEFINITION: The largest integer that can evenly divide into all of the numbers in a set of numbers.

• There are two methods we can use to find the greatest common factor of two or more numbers…

• METHOD 1: MAKE A LIST

• List all the factors of each number. Circle the greatest factor that appears in the lists.

METHOD 1: MAKE A LIST

List all the factors of each number. Circle the greatest factor that appears in the lists.

Example 1: Find the greatest common factor of 12 and 18

Factors of 12: _____________________________

Factors of 18: _____________________________

Greatest Common Factor of 12 and 18: __

1, 2, 3, 4, 6, 12

1, 2, 3, 6, 9, 18

6

METHOD 1: MAKE A LIST

List all the factors of each number. Circle the greatest factor that appears in the lists.

Example 2: Find the greatest common factor of 12, 18, and 24

Factors of 12: _____________________________

Factors of 18: _____________________________

Factors of 24: _____________________________

Greatest Common Factor of 12, 18, and 24: __

1, 2, 3, 4, 6, 12

1, 2, 3, 6, 9, 18

1, 2, 3, 4, 6, 8, 12, 24

6

METHOD 2: Upside Down Cake

Example 1: Find the GCF(12,32)

Greatest Common Factor of 12 and 32: __

2

12 32

6 16

2

Since 3 and 8 share no common factors, stop here!

3 8

Multiply the circled numbers

4

METHOD 2: Upside Down Cake

Example 1: Find the GCF(32,96)

Greatest Common Factor of 12 and 32: ___

2

32 96

16 48

2

2

8 24

4 12

2

2 6

2

Since one of your numbers is now 1, stop here!

1 3

32

METHOD 2: Upside Down Cake

Example 2: Find the GCF(30,48,120)

Greatest Common Factor of 30,48,120: ___

2

30 48 120

If 2 doesn’t work, go on to the next number

15 24 60

3

Since your numbers share no common factors, stop here!

5 8 20

6

Mr. Grover wants to make shelves for his garage using an 18-foot board and a 36-foot board. He will cut the boards to make shelves of the same length and wants to use all of both boards. Find the greatest possible length of each shelf.