Transcript Lesson 3.1 - Hood River County School District

Lesson 3.1
Core Focus on Decimals
& Fractions
Greatest Common Factor
Warm-Up
1. Write three multiplication problems
using whole numbers that equal 20.
1  20
2  10
45
2. Find the value of 3 × 5.
15
3. Find the value of 6 × 7.
42
Lesson 3.1
Greatest Common Factor
Find the greatest common factor
(GCF) of a set of numbers.
Vocabulary
Factors
Numbers that can be multiplied to find a product.
Prime Number
A whole number that has only two possible factors (1 and itself).
Composite Number
A whole number larger than one with more than two factors.
Example 1
Determine if 12 is a prime or composite number.
List the pairs of numbers that
have a product of 12.
1 × 12
2×6
3×4
12 × 1
6×2
4×3
These are the same as
the first column but in
reverse order
List each factor once, even
if it is repeated.
1, 2, 3, 4, 6, 12
The factors of 12 are 1, 2, 3, 4, 6, and 12. There are more
than two factors so the number 12 is composite.
Vocabulary Continued…
Greatest Common Factor
The greatest factor that is a whole number common to all the
numbers.
Explore!
University Sales
Bracken had 36 University of Miami shirts and 42 Florida State University shirts to
sell. He wants to stack them in piles that would all have the same number of shirts.
He does not want to mix the two types of shirts. What is the greatest number of shirts
that can be stacked in each pile? Find the GCF of 36 and 42.
Step 1
Find all factors of 36 by filling the boxes with the missing factors.
Make a list of all factors of 36.
  36
Step 2
  12
4
6
Find all factors of 42 by filling the boxes with the missing factors.
Make a list of all factors of 42.
1
Step 3
2
2
3
7
Circle the common factors. Common factors are factors that are the same
for both 36 and 42.
Explore!
Step 4
Draw a Venn diagram like the one below on a sheet of paper.
Write “Factors of 36” on the outside of the left circle and
“Factors of 42” on the outside of the right circle.
Factors of 36
Step 5
University Sales
Factors of 42
Write all factors in the Venn diagram. Write the factors that both numbers
have in common in the overlapping part of the circles. The remaining factors
of 36 should be written in the yellow part of the left circle. The remaining
factors of 42 should be written in the pink part of the right circle.
Explore!
University Sales
Step 6
Look at the common factors written in the overlapping part of the circles in
the Venn diagram. Circle the largest number. This is the greatest common
factor (GCF).
Step 7
Use the GCF to answer the question in the problem at the beginning of the
Explore! in a complete sentence.
Step 8
Repeat Steps 1–6 to find the GCF of the following pairs of numbers:
a. 15 and 25
b. 18 and 30
c. 24 and 40
Vocabulary Continued…
Prime Factorization
A composite number written as a product of all its prime factors.
Example 2
Two local teams went to soccer camp together. At the camp the teams were
asked to split into equal amounts for cabin groups. The players did not want
to room with players from other teams. The camp directors want the largest
number possible in each cabin. How many players will be in each cabin?
Team 1
36 Players
Team 2
30 Players
Use prime factors to find the GCF. Prime factors are factors that are
prime numbers.
36
Write each number as products
of two factors.
4
Continue to write each number as
products of two factors until only
factors that are prime numbers
remain.
22

30
9
6
33
23

5
5
Example 2 Continued…
Two local teams went to soccer camp together. At the camp the teams were
asked to split into equal amounts for cabin groups. The players did not want
to room with players from other teams. The camp directors want the largest
number possible in each cabin. How many players will be in each cabin?
Team 1
36 Players
Team 2
30 Players
36
4
22

30
9
6
33
23

Write the factors out for each number.
This is called the prime factorization.
Highlight the common prime factors.
36 = 2  2  3  3
Find the product of the common prime
factors. This is the GCF.
GCF = 2  3 = 6. The GCF is 6.
Six players will be in each cabin.
5
5
30 = 2  3  5
Example 3
Reagan Middle School students were asked to sit in equal rows for the
assembly. There were 98 sixth graders, 84 seventh graders and 112 eighth
graders. The teacher did not want grade levels to sit together, but the rows
were to be as wide as possible. How many students should sit in each row?
List the factors of each number. Highlight the common factors.
Factors of 98: 1, 2, 7, 14, 49, 98
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Find the GCF.
Fourteen students should sit in each row.
Finding the Greatest Common
Factor
LIST
PRIME FACTORIZATION
1. List the factors for
each number.
1. Write each number as a
product of its prime factors.
2. Highlight the common
factors.
2. Highlight the common prime
factors.
3. Identify the GCF
(greatest common
factor).
3. Find the product of the
common prime factors to
identify the GCF (greatest
common factor).
Communication Prompt
What is a real life situation in which you would need to find the
greatest common factor?
Exit Problems
1. Find the GCF of 56 and 64.
8
2. Gina wants to sell 49 chocolate chip cookies and 35 sugar
cookies. She is going to sell them on plates with equal
amounts on each plate. Each plate needs to hold the largest
number of cookies without mixing types of cookies. How
many cookies should Gina put on each plate?
7 cookies