How do you use prime factorization to find the GCF or LCM of two whole numbers? For example, how do...
-
Upload
isabella-powers -
Category
Documents
-
view
223 -
download
0
Transcript of How do you use prime factorization to find the GCF or LCM of two whole numbers? For example, how do...
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
7 is a prime number. 7 x 1 = 7
Prime numbers have only two factors, one and themselves.
Composite numbers have more than two factors.
10 is a composite number. 1 x 10 = 10 2 x 5 = 10
The first few prime numbers are 2, 3, 5, 7, 11, 13, 17…
Let’s Review
Prime factorization is finding a string of prime numbers that when multiplied result in your
original number.40
factor tree
The first few prime numbers are 2, 3, 5, 7, 11, 13, 17…
2 x 20
2 x 10
2 x 5
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.
25, 50, 75…1, 5, 25
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?
8factor tree
2 x 4
2 x 2
= 2 x 2 x 2 30
2 x 15
3 x 5
= 2 x 3 x 5
Core Lesson
8= 2 x 2 x 2 30= 2 x 3 x 5
Venn Diagram
22 2 3 5
GCF
LCM
The GCF of 8 and
30 is 2.
The LCM of 8 and 30 is 120.
2 x 2 x 2 x 3 x 5 = 120
Core Lesson
What is the GCF and LCM of 18 and 27?
18
2 x 9
= 2 x 3 x 3 27
3 x 9
3 x 3
= 3 x 3 x 3
3 x 3
Core Lesson
18= 2 x 3 x 3 27= 3 x 3 x 3
Venn Diagram
3 3
GCF
LCM
The GCF of 18 and 27 is 9.
The LCM of 8 and 30 is 54.
2 x 3 x 3 x 3 = 54
3
3 x 3 = 9
2