Download 5.3 Finding the GCF

List the factors of the following numbers.
5
15
48
82
100
51
17 3
20
6
-6
5
-1
49
7 7
14
In each diagram below, write the two numbers on the
sides of the “X” that are multiplied together to get the top
number of the “X,” but added together to get the bottom
number of the “X.”
Foundations of Algebra
UNIT QUESTION: In what ways can
algebraic methods be used in
problems solving?
Standard: MM1A2
Today’s Question:
How do we find the GCF of a
polynomial?
Standard: MM1A2f
GCF
What does it stand for?
What is it?
What do these have in common??
What do these have in common??
A prime number is a
number that can be divided by only
one and itself.
A composite number is a number
greater than one that is not prime.
Prime or composite?
37
prime
51
composite
To find the prime factorization of a number,
write the number as the product of prime
numbers.
Find the prime factorization of 84.
84
2
42
2
21
3
7
Find the prime factorization of 100.
100
10
2
10
5
2
5
The greatest common factor (GCF) of two
natural numbers is the largest number that is a
factor of both numbers.
Example:
84 = 2 x 2 x 3 x 7
100 = 2 x 2 x 5 x 5
GCF = 2 x 2 = 4
Find the GCF of 84 and 180.
84 = 2 x 2 x 3 x 7
180 = 2 x 2 x 3 x 3 x 5
GCF = 2 x 2 x 3 = 12
GCF with Variables
Note: With variables, the GCF will
always be the smallest exponent of a
common variable
Examples:
12x3, 16x2
GCF = 4x2
45a5, 50a7
GCF = 5a5
6. What is the greatest common
factor??
5a
35
7. What is the greatest common
factor??
3y
-8xy
8. What is the greatest common
factor??
2
22x
-11x
Note: With negatives, go by the leading term!!
9. What is the greatest common
factor??
6
-4x ,
4
-x ,
2
-2x
2
-x
Note: With negatives, go by the leading term!!