Download WNDI Prime Factorization

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Lesson 10: Prime Factorization
A prime number is a whole number greater than 1 whose only factors are
1 and itself. A composite number is a whole number greater than 1 that has
factors other than 1 and itself. You can write any composite number as a
product of prime numbers, which is called its prime factorization.
EXAMPLE 1
Tell whether the numbers 19 and 21 are prime or composite.
The only factors of 19 are 1 and 19. So, 19 is prime.
The factors of 21 are 1, 3, 7, and 21. So, 21 is composite.
EXAMPLE 2
Write the prime factorization of 60.
1.1.WHOLE
WHOLENUMBERS
NUMBERS
10.
1. Place
Prime
Value
Factorization
Whole Numbers, Decimals,
and Integers
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Use a diagram called a factor tree. Write 60 at the top. Draw two branches
and write 60 as the product of two factors. Continue to draw branches
until all the factors are prime numbers. Here are two factor trees for 60.
2
60
3
2
30
3
3
15
3
5
HINT
You can start a
factor tree with any
two factors of the
number.
60
6
2
3 3
10
3
2 3 5
Both factor trees show that the prime factorization of 60 is 22 3 3 3 5.
Practice: First Try
List all factors of the number. Tell whether it is prime or composite.
1. 13
2. 27
3. 32
4. 41
5. 49
6. 55
Draw a factor tree for the number. Write its prime factorization.
7. 36
8. 50
9. 54
McDougal Littell Middle School Math
Remediation Book Lesson 1.10
19
LESSON 00.00
1. WHOLE NUMBERS
More Copy if Needed
10. Prime Factorization
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Practice: Second Try
List all factors of the number. Tell whether it is prime or composite.
1. 16
2. 42
3. 23
4. 35
5. 39
6. 26
Draw a factor tree for the number. Write its prime factorization.
7. 30
8. 24
10. 44
11. 81
9. 63
12. 100
13. Every prime number besides 2 is an odd number.
14. Every positive even number besides 2 is composite.
15. Every odd number greater than 1 is prime.
Extend Your Skills
16. List the first 20 prime numbers. (The number 1 is neither prime nor composite.)
Puzzle
Write 100 as the sum of two primes in six different ways.
100 5 ? 1 ?
20
McDougal Littell Middle School Math
Remediation Book Lesson 1.10
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
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