Download Lesson 4-3 - lvocciomath

Name
Class
Date
Lesson 4-3
Prime Numbers and Prime Factorization
NAEP 2005 Strand: Number Properties and Operations
Topic: Properties of Number and Operations
Lesson Objective
To factor numbers and to find the prime
factorization of numbers
Local Standards: ____________________________________
Vocabulary.
A factor is
All rights reserved.
A composite number is
A prime number is
A prime factorization is
Example.
1 Finding Factors List the factors of each number.
a. 24
1 ! 24
2!
,3!
,4!
d
6!
,
, and
are factors. Skip 5, since 24 is not divisible by 5.
d Stop when you repeat factors.
The factors of 24 are
,
,
,
,
,
,
, and
.
b. 35
1 ! 35
d Write each pair of factors. Start with 1.
! 7 d Skip 2, 3, and 4, since 35 is not divisible by 2, 3, or 4.
Skip 6, since 35 is not divisible by 6.
7!
is a factor.
d Stop when you repeat factors.
The factors of 35 are
,
,
, and
.
Quick Check.
1. A gift box must hold the same number of pears in each row. You have 24
pears. What arrangements can you use?
54
Course 1 Lesson 4-3
Daily Notetaking Guide
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
d Write each pair of factors. Start with 1.
Name
Class
Date
Examples.
2 Prime or Composite? Is the number prime or composite? Explain.
a. 61
; 61 has
b. 65
; 65 is divisible by
factors,
and
.
, so 65 has more than
factors.
3 Prime Factorization Write the prime factorization of 90 using exponents.
All rights reserved.
Method 1 Use a division ladder
2 90
d Divide 90 by the prime number 2. Work down.
3
d The result is
. Divide by the prime number 3.
3
d The result is
. Divide by 3 again.
d The prime factorization is
!
.
!
Method 2 Use a factor tree
d Since the sum of the digits of
90
90 is 9, 90 is divisible by 3.
90 " 3 !
S
d
30 " 3 !
S
d
10 " 2 ! 5
S
d
The prime factorization of 90 is
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
!
!
!
!
Circle the prime numbers
as you find them.
, or
!
2
!
.
Quick Check.
2. Is the number prime or composite? Explain.
a. 39
b. 47
c. 63
3. Find the prime factorization of 27.
Daily Notetaking Guide
Course 1 Lesson 4-3
55