Download Greatest Common Factor (GCF)

EOC Warm Up #5
Objectives
The student will be able to:
1. find the prime factorization of a number.
2. find the greatest common factor (GCF) for
a set of monomials.
3. Factor using the greatest common factor
(GCF).
A prime number is a
number that can only 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
Prime or Composite?
89
1.
2.
3.
4.
Prime
Composite
Both
Neither
1) Find the prime factorization of 84.
84
=
=
=
4 • 21
2•2•3•7
22 • 3 • 7
2) Find the prime factorization of -210.
-210= -1 • 210
= -1 • 30 • 7
= -1 • 6 • 5 • 7
= -1 • 2 • 3 • 5 • 7
3) Find the prime factorization of
45a2b3
45a2b3 =
9•5•a•a•b•b•b
= 3•3•5•a•a•b•b•b
= 32 • 5 • a • a • b • b • b
Write the variables without exponents.
What is the prime factorization of 48?
1.
2.
3.
4.
3
3
2
2
16
4 4
2 3 4
2 2 2 3
The Greatest Common Factor
(GCF) of 2 or more numbers is
the 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.
42 = 2 • 3 • 7
60 = 2 • 2 • 3 • 5
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!
5) Find the GCF of 40a2b and 48ab4.
40a2b = 2 • 2 • 2 • 5 •
a•a•b
48ab4 = 2 • 2 • 2 • 2 • 3 • a • b • b • b • b
What do they have in common?
Multiply the factors together.
GCF = 8ab
What is the GCF of 48 and 64?
1.
2.
3.
4.
2
4
8
16
6): What is the GCF of
25a2 and 15a?
5a
Let’s go one step further…
1) FACTOR 25a2 + 15a.
Find the GCF and divide each term
25a2 + 15a = 5a( ___
5a + ___3 )
25a 2
5a
15a
5a
Check your answer by distributing.
7) Factor 18x2 - 12x3.
Find the GCF
6x2
Divide each term by the GCF
18x2 - 12x3 = 6x2( ___
3 - ___
2x )
18 x 2
6x2
12 x3
6x2
Check your answer by distributing.
8) Factor
2
28a b
+
2
56abc .
GCF = 28ab
Divide each term by the GCF
28a2b + 56abc2 = 28ab ( ___
a + ___
2c)2
28a 2b
28ab
56abc 2
28ab
Check your answer by distributing.
28ab(a + 2c2)
Factor
1.
2.
3.
4.
x(20 – 24y)
2x(10x – 12y)
4(5x2 – 6xy)
4x(5x – 6y)
2
20x
- 24xy
9) Factor 28a2 + 21b - 35b2c2
GCF = 7
Divide each term by the GCF
28a2 + 21b - 35b2c2 = 7 ( ___
4a2 + ___
3b- ____
5b2)c2
28a 2
7
21b
7
35b 2 c 2
7
Check your answer by distributing.
7(4a2 + 3b – 5b2c2)
Factor
1.
2.
3.
4.
2
16xy
2y2(8x – 12z + 20)
4y2(4x – 6z + 10)
8y2(2x - 3z + 5)
8xy2z(2 – 3 + 5)
-
2
24y z
+
2
40y