1. Do Now 12/1/09 Take out HW from last night. Copy HW in your planner.
Text page 175, #16-44 multiples of 4; #48-54 evens
Copy HW in your planner.
Text page 179, #12-46 evens
“Pop-Quiz” tomorrow
In your journal, explain what a FACTOR is in your own words. Then give an example of a factor. What do you think the definition of the GREATEST COMMON FACTOR is?

2. Homework Text page 175, #16-44 multiples of 4; #48-54 evens
16) 1, 2, 4, 8
20) 1, 2, 3, 4, 6, 9, 12, 18, 36
24) prime
28) composite
32) row 2: 13; row 3: 4, 13; row 4: 2; 2³ · 13
36) 3² · 7
40) 2 · 7 · 11
44) 7 · 31
48) 11 · c · d
50) 3 · f · f · f · f · f · f
52) 5 · x · y · y
54) 2 · y · y · y · y · z · z · z

3. Objective
SWBAT find the greatest common factor of two or more whole numbers

4. Section 4.2 “Greatest Common Factor”
a number that is multiplied in an expression.
Example: · 4 = 8
product
factor
factor
Do you know all the factors of 8?
8: 1, 2, 4, 8

5. Section 4.2 “Greatest Common Factor”
The common factor of two numbers.
LARGEST
Find the GCF of 8 and 12.
List the factors of the two numbers and then compare.
8: 1, 2, 4, 8
12: 1, 2, 3, 4, 6, 12
From the list you can see that 1, 2, and 4 are common factors.
Of these 4 is the greatest common factor.

6. Greatest Common Factors
Find the GCF of 12, 18, and 30.
List the factors of the three numbers and then compare.
12: 1, 2, 3, 4, 6, 12
18: 1, 2, 3, 6, 9, 18
30: 1, 2, 3, 5, 6, 10, 15, 30
From the list you can see that 1, 2, 3, and 6 are common factors.
Of these 6 is the greatest common factor.

7. Greatest Common Factors
Find the GCF of 180 and 378.
When the numbers are too large to list the factors
of the two numbers, find the prime factorization of each
and then compare.
180: 2 · 2 · 3 · 3 · 5
378: 2 · 3 · 3 · 3 · 7
From the list you can see that 2, 3, and 3 are common prime
factors. The greatest common factor of 180 and 378 is the
product of 2 · 3 · 3 which is 18.

8. Greatest Common Factors
Find the GCF of 39 and 50.
When the numbers are too large to list the factors
of the two numbers, find the prime factorization of each
and then compare.
Relatively Prime:
Two numbers are relatively
prime if their greatest common
factor is 1.
39: 3 · 13
50: 2 · 5 · 5
From the list you can see that there are NO common prime
factors. However, two numbers always have 1 as a common factor. So the GCF is 1 and the two numbers are relatively prime.

9. GCF of Variable Expressions
Find the GCF of 12x²y and 6xy³.
Write the prime factorization of each and then compare.
12x²y: · 2 · 3 · x · x · y
6xy³: · 3 · x · y · y · y
From the list you can see that 2, 3, x, and y are common prime
factors. The greatest common factor is the
product of 2 · 3 · x · y, which is 6xy.

10. GCF of Variable Expressions
Find the GCF of 18xy² and 28x²y³.
Write the prime factorization of each and then compare.
18xy²: · 3 · 3 · x · y · y
28x²y³: · 2 · 7 · x · x · y · y · y
From the list you can see that 2, x, y, and y are common prime
factors. The greatest common factor is the
product of 2 · x · y · y, which is 2xy².

11. 24
Homework
Text page 179, #12-46 evens