Download 4.4 Greatest Common Factor.notebook

4.4 Greatest Common Factor.notebook
October 30, 2012
Finding the Greatest Common Factor
IAN pg. 65
Greatest Common Factor (GCF) is the greatest factor in common of all numbers.
Warm­up 10/31/12
IAN pg. 64
Example find the GCF of 24 and 36.
Method 1 ­ Listing Factors
Step 1: List all factors of both numbers
Factors of 24:
Factors of 36:
Step 2: Identify greatest common factor.
Identify the following numbers as prime or composite.
1. 4
3. 7
*This method not best for large numbers with a lot of factors.
2. 6
4. 1
Method 2 ­ Prime Factorization (Factor Tree)
Step 1: Write Prime Factorization of both numbers.
24
36
Step 2: Find product of all common factors.
*If two same factors repeat multiply them that number of times.
24: 2 x 2 x 2 x 3 2 x 2 x 3 = 12
36: 2 x 2 x 3 x 3
You Try:
IAN pg. 64
Find the GCF for:
A. 16 and 56
B. 6, 8, 12
Finding the GCF of Monomials
Two bands are marching at an event. There are 32 members on one band and 40 on the other. They are marching in rows of equal size that are as wide as possible. How many people are in each row?
IAN pg. 64
IAN pg. 65
You can use either Method 1 or 2
You Try:
Example: GCF of 36x3y and 56xy2
Method 1: List all factors of each #.
Step 1: List factors.
36x3y:
56xy2:
IAN pg. 64
Find the GCF of each set.
A. 32mn2, 16n, 12n3
B. 18a, 30ab, 42b
Step 2: Identify GCF and shared variables.
*Both monomials must share variable in order to factor out to GCF.
Method 2 ­ Prime Factorization
Step 1: Write Prime Factorization for each #.
56xy2
36x3y
Step 2: Find product of shared prime factors and variables.
1
4.4 Greatest Common Factor.notebook
Factoring Expressions
IAN pg. 65
Ex. 8v + 56
October 30, 2012
Homework: Workbook pg. 24 odds
Step 1: Identify GCF
Step 2: Factor out (divide) GCF from each term.
8v + 56; GCF =
2