Chapter 7 7-2 Factoring by GCF. Objectives Factor polynomials by using the greatest common factor.
Objectives The student will be able to: find the greatest common factor (GCF) for a set of...
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Transcript of Objectives The student will be able to: find the greatest common factor (GCF) for a set of...
ObjectivesThe student will be able to:
find the greatest common factor (GCF) for a set of monomials.
The Greatest Common Factor (GCF) of 2 or more numbers isthe largest number that can divide
into all of the numbers.
4) Find the GCF of 42 and 60.
Write the prime factorization of each number.
4) Find the GCF of 42 and 60.
What prime factors do the numbers have in common?
Multiply those numbers.
The GCF is 2 • 3 = 6
6 is the largest number that can go into 42 and 60!
42 = 2 • 3 • 760 = 2 • 2 • 3 • 5
What is the GCF of 48 and 64?
1. 2
2. 4
3. 8
4. 16
Think Backwards…
• Find Factors
• Circle Common Factors
• Group Greatest Factor
Step 1: Find the Factors
• 24 – 1,2,3,4,6,8,12,24
• 36 – 1,2,3,4,6,9,12,18,36
Step 2: Circle Common Factors
• 24 – 1,2,3,4,6,8,12,24
• 36 – 1,2,3,4,6,9,12,18,36
Step 3: Group the Greatest Factor
• 24 – 1,2,3,4,6,8,12,24
• 36 – 1,2,3,4,6,9,12,18,36
The Greatest Common Factor of 24 and 36 is…
12
The Greatest Common Factor of 24 and 36 is…
12
What is the GCF of 18 and 27?
18 27
1 x 18
2 x 9
3 x 6
4 x ?
5 x ?
6 x 3
Factors of 18:
1, 2, 3, 6, 9, 18 1 x 27
2 x ?
3 x 9
4 x ?
5 x ?
6 x ?
7 x ?8 x ?
9 x 3
Factors of 27:
1, 3, 9, 27
Common Factors: 1, 3, 9
GCF: 9
Ex: Find the GCF(24, 40) Prime Factorizations
24
22
126
24 = 2 * 2 * 2 * 3
40
2 202 102 5
40 = 2 * 2 * 2 * 5
2 3
Ex: Find the GCF(32, 51)
Prime Factorization:
32
22
168
32 = 2 * 2 * 2 * 2 * 2
51
3 17
51 = 3 * 172 42 2
Ex: Find the GCF(102, 84)
Prime Factorization:
102
23
5117
32 = 2 * 3 * 17
84
3
42
51 = 2 * 2 *3 * 7
2
2 217