Download Write Numbers Using Prime Factorization

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Determine
the prime factors of all numbers through 50 and write
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UNDERLYING SKILLS AND CONCEPTS:
numbers as the product of their prime factors using exponents
to show multiples of a factor (e.g., 24 ! 2 " 2 " 2 " 3 ! 8 x 3).
recognize prime numbers;
use associative property for
multiplication;
write numbers with exponents
Write Numbers Using Prime Factorization
You can write a number as the product of its prime factors.
You can make a factor tree to write a number in
prime factorization.
Divisibility Rules can help.
I love trees.
E x am p l E
1
Make a factor tree. This is the simplest way to make a factor tree.
Step 1: Find the smallest number (greater than one) that evenly divides 12.
Step 2: How many times does 2 go into 12? 6 times. So 12 ! 2 " 6.
Step 3: Now find the smallest number that evenly divides 6: 2. So, 6 ! 2 " 3.
Step 4: Can you find a number greater than 1 that evenly divides 3? No.
So stop.
12 is even
The prime factorization of 12 is 12 ! 2 " 2 " 3.
so 2 is a factor.
This is also represented as:
12 ! 22 " 3.
12
6 is even
Notice that the product of the factors in each row in the
so 2 is a
factor tree is equal to the number you are factoring.
2 " 6 factor again.
2
E x am p l E
"
3
2
Write 36 as a product of prime factors.
Make a factor tree. If you know of any number that evenly divides 36, start with it.
You can start with 2, 3, 4, 6, 9, or 18.
Circle the prime factors as you find them.
Write the number as a product of prime factors.
36 ! 3 " 3 " 2 " 2, or 32 " 22
36
6
2
page 92
6
3 2
Tree or root?
3
Chapter 8 – Lesson 4
E – © CSL Associates, Inc. All rights reserved.
Find the prime factorization of 12.
Name
P RAC T I C E
Make a factor tree for each number in the box next to the number.
Then write the prime factorization for each number. Use square and cube numbers when you can.
1. 10
2. 20
3. 72
25
22 5
23 32
Write an equation for each situation. Then solve.
4. Jason had 3 bags. Each bag had 3 packs of gum in it.
Each pack of gum had 5 pieces.
How many pieces of gum did Jason have?
3 3 5 32 5 45
E – © CSL Associates, Inc. All rights reserved.
5. Mrs. Kee bought a gross of pencils (144 pencils). She divided them
among 3 classrooms. Each classroom had 24 students. How many
pencils did she buy for each student? 144 (3 24) 144 72 2
Circle the correct choice.
6. Which is NOT another way to write 56?
A
B
C
D
96
87
23 7
65 – 9
7. Which is another way to write 96?
F
G
196
32 6
H
J
25 3
24 32
Write the prime factorization of each number.
8. 27
3 3 3 33
10. 101
101
9. 78
2 3 13
11. 84
22 3 7
Math
Reasoning
Title
MR 2.2, 2.6
Solve. Explain how you decided.
12. I am a whole number. My prime factorization is 24 3. Who am I?
48 because 2 2 2 2 3 48.
Chapter 8 – Lesson 4
page 93
MCX94.HW.CL.G5.FM&Lesson.v211
8/2/04
18:02
Page 64
Name
…at home!
P RAC T I C E
Make a factor tree for each number in the box next to the number.
Then write the prime factorization for each number. Use square and cube numbers when you can.
1. 16
2. 27
3. 48
24
33
24 3
Write an equation for each situation. Then solve.
4. Mike had 4 bags. Each bag had 4 packs of peppermint sticks in it.
Each pack of peppermint sticks had 6 sticks.
How many peppermint sticks did Mike have?
4 4 6 42 6 96
among 4 classrooms. Each classroom had 18 students. How many
pens did she buy for each student? 144 (4 18) 144 72 2
Circle the correct choice.
6. Which is NOT another way to write 54?
A
96
B
87
C
D
2 33
60 – 6
7. Which is another way to write 45?
F
G
145
32 5
H
J
32 5
23 5
Write the prime factorization of each number.
8. 36
22 32
10. 103
1 103
9. 75
3 52
11. 96
25 3
Math
Reasoning
Title
MR 2.2, 2.6
Solve. Explain how you decided.
12. I am a whole number. My prime factorization is 2 33. Who am I?
54 because 2 3 3 3 54.
page 64
Home Resource and Homework
Chapter 8 Lesson 4
E – © CSL Associates, Inc. All rights reserved.
5. Mrs. Cooper bought a gross of pens (144 pens). She divided them
MCX94TEG5CH01_32.v7.4.2 2/24/01 19:44 Page 173
Name
P RAC T I C E
Make a factor tree for each number in the box next to the number.
Then write the prime factorization for each number. Use square and cube numbers when you can.
1. 10
2. 20
3. 72
20
72
10
2
2
5
10
2
2
36
2
5
18
2
Possible
Answer
Possible
Answer
25
9
Possible 3
Answer
22 5
3
23 32
Write an equation for each situation. Then solve.
4. Jason had 3 bags. Each bag had 3 packs of gum in it.
Each pack of gum had 5 pieces.
How many pieces of gum did Jason have?
3 3 5 32 5 45
E – © CSL Associates, Inc. All rights reserved.
5. Mrs. Kee bought a gross of pencils (144 pencils). She divided them
among 3 classrooms. Each classroom had 24 students. How many
pencils did she buy for each student? 144 (3 24) 144 72 2
Circle the correct choice.
6. Which is NOT another way to write 56?
A
B
C
D
96
87
23 7
65 – 9
7. Which is another way to write 96?
F
G
196
32 6
H
J
25 3
24 32
Write the prime factorization of each number.
8. 27
3 3 3 33
10. 101
101
9. 78
2 3 13
11. 84
22 3 7
Math
Reasoning
Title
MR 2.2, 2.6
Solve. Explain how you decided.
12. I am a whole number. My prime factorization is 24 3. Who am I?
48 because 2 2 2 2 3 48.
Chapter 8 – Lesson 4
Student Book Page
page 93
Name
…at home!
P RAC T I C E
Make a factor tree for each number in the box next to the number.
Then write the prime factorization for each number. Use square and cube numbers when you can.
1. 16
2. 27
3. 48
27
48
16
4
2
3
4
2 2
9
3
2
2
2
3
24
12
2
6
Possible
3
Answer 2
Possible
Answer
Possible
Answer
24
33
24 3
Write an equation for each situation. Then solve.
4. Mike had 4 bags. Each bag had 4 packs of peppermint sticks in it.
Each pack of peppermint sticks had 6 sticks.
How many peppermint sticks did Mike have?
4 4 6 42 6 96
among 4 classrooms. Each classroom had 18 students. How many
pens did she buy for each student? 144 (4 18) 144 72 2
Circle the correct choice.
6. Which is NOT another way to write 54?
A
96
B
87
C
D
2 33
60 – 6
7. Which is another way to write 45?
F
G
145
32 5
H
J
32 5
23 5
Write the prime factorization of each number.
8. 36
22 32
10. 103
1 103
9. 75
3 52
11. 96
25 3
Math
Reasoning
Title
MR 2.2, 2.6
Solve. Explain how you decided.
12. I am a whole number. My prime factorization is 2 33. Who am I?
54 because 2 3 3 3 54.
page 64
Home Resource and Homework
Chapter 8 Lesson 4
E – © CSL Associates, Inc. All rights reserved.
5. Mrs. Cooper bought a gross of pens (144 pens). She divided them