Download 2013-09-19.00-13-54-20130820_1453_findthegcf_lessonslides_ppt

How do you use prime
factorization to find the GCF or
LCM of two whole numbers?
For example, how do you use prime
factors to find the GCF and LCM
of 8 and 30?
In this lesson you will learn
how to find the GCF and LCM
of two whole numbers by
using their prime factors.
Let’s Review
Prime numbers have only two factors,
one and themselves.
7 is a prime number. 7 x 1 = 7
The first few prime numbers are 2, 3, 5, 7, 11, 13, 17…
Composite numbers have more than two
factors.
10 is a composite number.
1 x 10 = 10
2 x 5 = 10
Let’s Review
factor tree
40
2 x 20
2 x 10
2x5
The first few prime numbers
are 2, 3, 5, 7, 11, 13, 17…
Prime factorization is finding a
string of prime numbers that
when multiplied result in your
original number.
40 = 2 x 2 x 2 x 5
All composite numbers can
be written as a string of
prime factors.
A Common Misunderstanding
Confusing factors with multiples
Find the factors of 25.
1, 5, 25
25, 50, 75…
A Common Misunderstanding
Remembering to find only prime
factors for a number when using
prime factorization.
The prime factors of 20 are 2 x 10.
Core Lesson
How do you use prime factorization
to find the GCF and LCM of 8 and 30?
factor tree
8= 2 x 2 x 2
30 = 2 x 3 x 5
2x4
2x2
2 x 15
3x5
Venn Diagram
Core Lesson
The
GCF of
8 and
30 is
2.
8= 2 x 2 x 2
2
LCM
2
GCF
2
30 = 2 x 3 x 5
3
5
2 x 2 x 2 x 3 x 5 = 120
The
LCM of
8 and
30 is
120.
Core Lesson
What is the GCF and LCM of 18 and 27?
18 = 2 x 3 x 3
2x9
3x3
27 = 3 x 3 x 3
3x9
3x3
Core Lesson
Venn Diagram
GCF 3 x 3 = 9
The
GCF of
18 and
27 is
9.
27 = 3 x 3 x 3
18 = 2 x 3 x 3
2
LCM
3 3
3
2 x 3 x 3 x 3 = 54
The
LCM of
8 and
30 is
54.
In this lesson you have
learned how to find the GCF
and LCM of two whole
numbers by using their prime
factors.