Name
LESSON
8-1
Date
Class
Reteach
Factors and Greatest Common Factors
A prime number has exactly two factors, itself and 1. The number 1 is not a prime number.
To write the prime factorization of a number, factor the number into its prime factors only.
Find the prime factorization of 30.
Choose any prime number that is a
factor of 30. Then divide.
5 30
6
5 30
5 30
26
5 30
26
3
5 30
26
33
5 30
26
33
1
30 ⫽ 5 · 2 · 3
Repeat the process with the quotient.
The prime factorization of 30 is 2 ⭈ 3 ⭈ 5.
Find the prime factorization of 84.
2 84
2 42
3 21
77
1
Check by multiplying:
2 · 2 · 3 · 7 ⫽ 84
2
The prime factorization of 84 is 2 ⭈ 2 ⭈ 3 ⭈ 7 or 2 ⭈ 3 ⭈ 7.
Fill in the blanks below to find the prime factorization of the given
numbers.
2 56
2 28
2. 2 14
7 7
1
2 44
22
1. 2
11 11
1
2 2 ⭈ 11
3 81
3 27
3.
3 9
3 3
1
34
23 ⭈ 7
Write the prime factorization of each number.
4. 99
5. 75
3 2 ⭈ 11
6. 84
3 ⭈ 52
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c08-1_rt.indd 6
6
22 ⭈ 3 ⭈ 7
Holt Algebra 1
12/26/05 8:13:12 AM
Process Black
Name
LESSON
8-1
Date
Class
Reteach
Factors and Greatest Common Factors (continued)
If two numbers have the same factors, the numbers have common factors.
The largest of the common factors is called the greatest common factor, or GCF.
Find the GCF of 12 and 18.
Think of the numbers you multiply to equal 12.
1 ⫻ 12 ⫽ 12
2 ⫻ 6 ⫽ 12
3 ⫻ 4 ⫽ 12
^
^
The factors of 12 are: 1, 2, 3, 4, 6, 12
Think of the numbers you multiply to equal 18.
1 ⫻ 18 ⫽ 18
2 ⫻ 9 ⫽ 18
3 ⫻ 6 ⫽ 18
The factors of 18 are: 1, 2, 3, 6, 9, 18.
The GCF of 12 and 18 is 6.
Find the GCF of 8x 2 and 10x.
The factors of 8x 2 are: 1, 2, 4, 8, x, x
The factors of 10x are: 1, 2, 5, 10, x
2
x
2
The GCF of 8x and 10x is 2x.
Find the GCF of 28 and 44 by following the steps below.
7. Find the factors of 28.
1, 2, 4, 7, 14, 28
8. Find the factors of 44.
1, 2, 4, 11, 22, 44
4
9. Find the GCF of 28 and 44.
Find the GCF of each pair of numbers.
10. 15 and 20
11. 16 and 28
12. 24 and 60
5
4
12
Find the GCF of each pair of monomials.
3
2
14. 15x and 21x
13. 4a and 10a
2a
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c08-1_rt.indd 7
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