Transcript 8-1 FindingGCF

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.
SOL: A.2c
Designed by Skip Tyler, Varina High School
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
What is the prime factorization
of 48?
1.
2.
3.
4.
3  16
344
2234
22223
3) Find the prime factorization of
45a2b3
(Factor the monomial completely)
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….
(Factor the monomial completely)
2
4
12g h
What is the prime factorization
of….
(Factor the monomial completely)
2
2
-38rp t
What is the prime factorization
of….
(Factor the monomial completely)
3
2
-17x y z
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 =
60 =
2 • 3 • 7
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!
Another Method
Find the GCF of 42 and 60.
What is the GCF of 48 and 64?
1.
2.
3.
4.
2
4
8
16
What is the GCF of 24 and 56?
1.
2.
3.
4.
8
6
3
4
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
3
2
24cd and48c d
What is the GCF of
2
15a b and35ab
2
What is the GCF of
2
26z ,32z,44z
4
Party Favors
• Balloons come in packages of 18 and
party hats come in packages of 8. You
want to have the same number of
balloons and hats. What is the fewest
packages of each you need to buy so
you have no hats or balloons left over?