Venn Diagrams and GCF’s
Objective: Students will be able to identify all factors for a pair of numbers
and use a Venn diagram to organize and identify the GCF of the two
numbers.
Background Knowledge: Students will need instruction on how to find all
factors for a number. Divisibility rules are also helpful.
Materials: A copy of the student worksheet for each child.
Directions/Activity: You may choose to do this as whole group, small
group, or individually
1. Distribute the worksheets to each child.
2. Have the students work through listing all of the factors for each
number.
3. Next, model for the students how to organize the numbers into the
Venn Diagrams.
4. Have the students identify the common factors by saying them out
loud.
5. Ask, “If these are all common factors, which would be considered the
Greatest Common Factor (GCF) and why?” Have them circle the
GCF.
6. Allow the students to complete the rest of the Venn diagram
questions.
7. You may want to check these as a whole group at the end of the
period.
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6th grade Unit 4
Venn-Diagram Factor Sheet
Find All Factors For Each Number By Using the Listing Method. List all
factors from Least to Greatest.
1.
12
2.
15
3.
48
4.
9
5.
30
6.
18
7.
24
8.
25
9.
27
10.
7
11. 42
12. 54
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6th grade Unit 4
Use the following Venn Diagrams to organize your work and find
the GCF for each pair of numbers.
1. Find the GCF of 12 and 18.
2. Find the GCF of 7 and 42. Draw your own Venn diagram.
3. Find the GCF of 48 and 24. Draw your own Venn diagram.
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6th grade Unit 4
4. Find the GCF of 18 and 30. Draw your own Venn diagram.
5. Find the GCF of 27 and 54. Draw your own Venn diagram.
6. Use the following diagram to find the GCF of 30, 27, and 24.
30
24
27
4
6th grade Unit 4
Key
1. 1x12 2x6 3x4 1,2,3,4,6,12
2. 1x15 3x5 1,3,5,15
3. 1x48 2x24 3x16 4x12 6x8 1,2,3,4,6,8,12,16,24,48
4. 1x9 3x3 1,3,9
5. 1x30 2x15 3x10 5x6 1,2,3,5,6,10,15,30
6. 1x18 2x9 3x6 1,2,3,6,9,18
7. 1x24 2x12 3x8 4x6 1,2,3,4,6,8,12,24
8. 1x25 5x5 1,5,25
9. 1x27 3x9 1,3,9,27
10. 1x7 1,7 (Prime)
11. 1x42 2x21 3x14 6x7 1,2,3,6,7,14,21,42
12. 1x54 2x27 3x18 6x9 1,2,3,6,9,18,27,54
1. left- 12, 4
center (common factors)-1,2,3,6
GCF=6
2. left-none
center (common factors)-1,7 right-2,3,6,14,21,42
GCF=7
3. left-48,16
4. left-18,9
center-1,2,3,4,6,8,12,24
GCF=24
center-1,2,3,6
GCF=6
right-18,9
right-none
right-10,15,30
5. left-none center-1,3,9,27 right-2,6,18,54
GCF=27
6. 24 and 30 share 1,2,3,6
30 and 27 share 1,3
27 and 24 share 1,3
They all share 1 and 3 so the GCF is 3
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6th grade Unit 4