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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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divisibility rules
Divisibility Rules
  • 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
divisibility rules1
Divisibility Rules
  • 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
common factors
Common Factors
  • 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

greatest common factor1
Greatest Common Factor
  • 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.
greatest common factor2
Greatest Common Factor

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

greatest common factor3
Greatest Common Factor

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

greatest common factor4
Greatest Common Factor

METHOD 2: Upside Down Cake

Example 1: Find the GCF(12,32)

Greatest Common Factor of 12 and 32: __

If you are “stuck” always start with 2

2

12 32

6 16

2

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

3 8

Multiply the circled numbers

4

greatest common factor5
Greatest Common Factor

METHOD 2: Upside Down Cake

Example 1: Find the GCF(32,96)

Greatest Common Factor of 12 and 32: ___

If you are “stuck” always start with 2

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

greatest common factor6
Greatest Common Factor

METHOD 2: Upside Down Cake

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

Greatest Common Factor of 30,48,120: ___

If you are “stuck” always start with 2

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

slide11

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.

Answer

18 foot boards

slide12

The SGB reps are making spirit ribbons. Blue ribbon comes in a 24 inch spool, red ribbon comes in a 30 inch spool, and gold ribbon comes in a 36 inch spool. The SGB reps want to cut strips of equal length, using the entire spool of each ribbon. What is the length of greatest piece of ribbon that can be cut from each spool?

Answer

6 inches

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