Transcript Prime Time 1.5

Prime Time 1.5
Objectives:
6.1E: Identify common factors and Greatest
Common Factor of a set of positive integers
6.1F: Identify common multiples and Least
Common Multiple of a set of positive integers
Venn Diagram
• What is a Venn Diagram?
• What does it look like?
• How do you use Venn Diagrams?
Definition
• Venn Diagram: a diagram in which
overlapping circles are used to show
relationships among sets of objects that
have certain attributes.
• This means a Venn Diagram shows what
groups have in common and what they
don’t!
Example
• In a Venn Diagram, group the whole
numbers from 1 to 9 according to whether
they are prime or multiples of 2.
• First, list the numbers that fall into each
category:
– Prime:
– Multiples of 2:
• Next, draw and label two overlapping
circles, one that represents the prime
numbers and one that represents the
multiples of 2. Draw a box around them.
• Then put each number from 1 to 9 in the
appropriate region.
• Hints:
– The numbers that don’t fall into either
category belong outside the circles.
– The numbers that are in both categories
belong in the overlap of the circles.
Example
• Using a T-Chart, list
the factors of 30 and
32.
• Create a Venn
Diagram and fill in all
whole numbers less
than or equal to 40.
Thirty
Thirty-two
Questions
• 1. What do the numbers in the
intersection (the “overlap”) of the circular
regions have in common?
• 2. List five numbers that fall in the region
outside the circles and explain why they
belong outside the circles?
• 3. What is the biggest number they both
have in common?
GCF
• The Greatest Common Factor of two
numbers is the largest factor the two
numbers share!
• GCF does not equal KFC.
• What is the GCF of 5 and 15?
• What is the GCF of 6 and 9?
Example
• List the multiples of 5
and the multiples of 2
that are less than or
equal to 30.
• Fill in a copy of a
Venn Diagram with
whole numbers less
than or equal to 30.
Five
Two
Questions
• What do the numbers in the intersection of
the circular regions have in common?
• List five more numbers that would be in
the intersection if numbers greater than 30
were allowed.
• Explain how you can use your completed
diagram to find the least multiple that 5
and 2 have in common.
LCM
• The Least Common Multiple of two
numbers is the smallest multiple two
numbers share!
• What is the LCM of 5 and 15?
• What is the LCM of 6 and 9?
Practice
1) Use a T-chart and a
Venn Diagram to
organize your
information. Find the
factors of 24 and 48.
What do they have in
common?
– List the factors of 24:
– List the factors of 48:
– Fill in the Venn
Diagram
– What is the GCF?
– Circle all prime #s
Twenty-four
Forty-eight
Practice
2) Use a Venn Diagram to
organize your
information. List the
multiples of 5 and 8. Use
all whole numbers, 1-45.
• List the multiples of 5
• List the multiples of 8
• Fill in the Venn Diagram
• Circle all Prime Numbers
• What is the LCM?
Five
Eight
Review!
• What are Venn Diagrams good for?
• What is the Greatest Common Factor?
• What is the Least Common Multiple?