Download 1.2 Prime Factorization

1.2
Prime Factorization
Lesson Objective
Vocabulary
Le
• Express a whole number as a product of its prime factors.
composite number
prime factor
arn Identify composite numbers.
Another way to represent a whole number is to write it as a product of its factors.
Find all the factors of 18.
18 5 1 3 18
18 5 2 3 9
18 5 3 3 6
The factors of 18 are 1, 2, 3, 6, 9, and 18.
The number 18 is an example of a composite number.
A composite number has more than two different whole number factors.
18 has six factors, so it is a composite number.
The number 3 is an example of a prime number. A prime number has only
two factors, the number itself and 1.
Le
In the list of factors for 18, 2 and 3 are the only prime numbers. 2 and 3 are the
prime factors of 18.
arn Write a composite number as a product of its prime factors.
A composite number can be written as
a product using only its prime factors.
This is known as prime factorization.
For example, you can write 18 as a product using
only its prime factors.
18 5 2 3 3 3 3
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Chapter 1 Positive Numbers and the Number Line
Math Note
Finding the prime factorization of a
number is not the same as finding
the factors of a number. A composite
number can be written as the
product of different pairs of its
factors. But there is one and only
one prime factorization for a given
composite number.
Express 60 as a product of its prime factors.
Method 1
Start dividing the number by
2
60
Divide by prime factor 2.
its least prime factor. Continue
30
2
Divide by prime factor 2.
dividing until the quotient is a
3
15
Divide by prime factor 3.
prime number.
5
The prime factors of 60 are 2, 3, and 5.
60 5 2 3 2 3 3 3 5
Method 2
60
2
·
30
·
2
·
2
·
2
·
2
Math Note
15
3
·
Another way to write multiplication
is to use the multiplication dot.
5
So, 60 5 2 · 2 · 3 · 5 means
60 5 2 3 2 3 3 3 5.
The prime factors of 60 are 2, 3, and 5.
60 5 2 · 2 · 3 · 5
Guided Practice
Complete.
1 Express 48 as a product of its prime factors.
Method 1
2
48
?
48
24
2
2
·
?
2
·
2
·
?
2
·
2
·
2
·
?
·
2
·
2
·
2
·
?
?
Method 2
6
?
48 5 2 3
?
323
?
3
?
2
48 5 2 · 2 · 2 · 2 ·
?
?
Lesson 1.2 Prime Factorization
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Practice 1.2
1 Copy the array of numbers. Circle all the prime numbers.
1
2
3
4
5
6
7
8
9
10
11
12
131415161718
192021222324
252627282930
Express each number as a product of its prime factors.
2 6
3 15
4 36
5 78
6 184
7 360
8 24
9 49
10 81
11 144
12 245
13 510
14 250
15 1,089
16 4,725
17 900
18 27,000
Solve.
19 Describe the steps for finding the prime factors of 42.
20 400 written as a product of its prime factors is 2 3 2 3 2 3 2 3 5 3 5.
Write 800 as a product of its prime factors.
21 Given that 320 written as a product of its prime factors is 2 3 2 3 2 3 2 3 2 3 2 3 5,
write 3,200 as a product of its prime factors.
22 2,700 written as a product of its prime factors is 2 3 2 3 3 3 3 3 3 3 5 3 5.
Write 270 as a product of its prime factors.
23 It is given that 4,800 can be expressed in terms of its prime factors as
2 3 2 3 2 3 2 3 2 3 2 3 3 3 5 3 5.
a) Write 1,200 as a product of its prime factors.
b) Now, write 120 as a product of its prime factors.
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Chapter 1 Positive Numbers and the Number Line