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Warmups
Multiply:
1.
(2 x  3)(4 x  1)
3.
Solve the system:
y  x4
3x  2 y  7
Subtract:
2.
(2 x  3)  (4 x  1)
10-1 FACTORS AND GREATEST
COMMON FACTORS
Objective: To find prime factorizations and
greatest common factors for monomials.
Standard 11.0
Factors


Factor: a number or variable that divides evenly into
your original number.
Example 1: Find the factors of 72.
 1
72
 2
36
 3
24
 4
18
 6
12
 8
9
This problem is like #19-23 in homework tonight!
Some terms to know
Prime: Only factors are 1 & itself
 Composite: Having more than 2 factors


Write the prime numbers up to 20:

1, 2, 3, 5, 7, 11, 13, 17, 19
FACTOR TREE (for composite #s)
384
2
192
2
96
2
48
2 24
2 12
2 6
2•2•2•2•2•2•2•3
2 3
Prime factorization
TOO
1) 20
2•2•5
2) 36
2•2•3•3
Hints
If it is an even, it is divisible by 2
If you add the digits and the answer is divisible
by 3, then the original number is divisible by 3
If it ends in 0 or 5, it is divisible by 5
Stop trying when the answer is smaller than the
number you divided by
FACTORING WITH VARIABLES
81b2c3
9 9
3 333

3•3•3•3•b•b•c•c•c
TOO
32abc3
2•2•2•2•2•a•b•c•c•c
GREATEST COMMON FACTOR (GCF)

Make a factor tree and multiply together what
they have in common
80
2
28
40
2
2 20
2 10
2 5
2•2 = 4 =GCF
14
2 7
GCF: Biggest number that will divide
evenly into all of the numbers

With variables, take the smallest exponent
32xy2z, 48x3y4
 2•2•2•2•2, 2•2•2•2•3


GCF: 16xy2

TOO for Homework

18xp2, 48x4
Challenge Problem – find the GCF
54a 2b
63a 2b2c
54a 2b 
63a 2b2c 
180ab3c2 
9ab
180ab3c 2
Homework

Greatest Common Factor Worksheet
Math Lab Warmups
Multiply:
1.
(5x - 4)
2
Subtract:
2.
(3x - 8) - (7x -1)
3.
(3x - 7)(2x + 5)
10-1 Prime Factorization
Example 1: Using a Factor Tree to Find Prime
Factorization
Write the prime factorization of the number.
A. 24
24
Write 24 as the product of
two factors.
8 · 3
4 · 2 · 3
Continue factoring until all
factors are prime.
2 · 2 · 2 · 3
The prime factorization of 24 is 2 · 2 · 2 · 3. Using
exponents, you can write this as 23 · 3.
Course 2
10-1 Prime Factorization
Example 2: Using a Factor Tree to Find Prime
Factorization
Write the prime factorization of the number.
B. 150
150
30 · 5
10 · 3 · 5
Write 150 as the product
of two factors.
Continue factoring until
all factors are prime.
2 · 5 · 3 · 5
The prime factorization of 150 is 2 · 3 · 5 · 5, or
2 · 3 · 52.
Course 2
2-4 Insert
Lesson Title Here
Prime Factorization
Try This: Example 3
Write the prime factorization of the number.
A. 36
36
Write 36 as the product of
two factors.
18 · 2
9 · 2 · 2
Continue factoring until all
factors are prime.
3 · 3 · 2 · 2
The prime factorization of 36 is 2 · 2 · 3 · 3. Using
exponents, you can write this as 22 · 32.
Course 2
10-1 Insert
Lesson Title Here
Prime Factorization
Try This: Example 4
Write the prime factorization of the number.
B. 90
90
45 · 2
9 · 5 · 2
Write 90 as the product
of two factors.
Continue factoring until
all factors are prime.
3 · 3 · 5 · 2
The prime factorization of 90 is 3 · 3 · 5 · 2, or
2 · 32 · 5.
Course 2
YOUR TURN! 

Prime Factorization Worksheet

Use scratch paper to make your factor trees.

Remember to list your factors in order from least
to greatest.

Work Individually

Switch and grade when everyone is done 