Download GCF and LCM Using Prime Factorization

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 =2x2x2
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=2x2x2
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.