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Name
Date
Class
Reteach
Factors and Greatest Common Factors
A prime number has exactly two factors, itself and 1. The number 1 is riot 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[3Q
5|30
2|6
5J30
^
3
5|30
_»
2[6_
3|3
5[30
2\6_
3[3_
-». 30 = 5 • 2 • 3
1
Repeat the process with the quotient.
The prime factorization of 30 is 2 • 3 • 5.
Find the prime factorization of 84.
2|84
242
3|21
7lZ
1
Check by multiplying:
2 • 2 • 3 • 7 - 84
V.
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|Q.
2|44
1 2Q
DQ
1
2-
DD
an
3|81
3-
an
DQ
DQ1
Write the prime factorization of each number.
4. 99
Copyright © by Holt, Rinehart and Winston.
ts reserved.
All rights
5. 75
6. 84
Holt Algebra 1
Name
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 X 12 = 12 '
2 X 6 = 12 >
The factors of 12 are: 1,2, 3, 4, 6, 12
3 x 4 = 12 i
Think of the numbers you multiply to equal 18.
1 X 1 8 = 18 '
2 X 9 = 18 >
The factors of 18 are: 1, 2, 3, 6, 9, 18.
3 X6 = 18 ,
The GCF of 12 and 18 is 6.
Find the GCF of 8x2 and 10x.
The factors of 8x2 are: 1, 2, 4, 8, x, x
The factors of 10x are: 1, 2, 5, 10, x
I
The GCF of 8x2 and 10x is 2x.
Find the GCF of 28 and 44 by following the steps below.
7. Find the factors of 28.
_
8. Find the factors of 44.
_
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
Find the GCF of each pair of monomials.
13. 4aand 10a
iht © by Holt, Rinehart and Winston.
All Vfghts reserved.
14. 15x3and21x2
15. 5y2 and 8y
Holt Algebra 1
Name
Date
Class.
isspFi Practice B
K£Ui Factors and Greatest Common Factors
~
Write the prime factorization of each number.
1. 18
2. 120
3. 56
4. 390
5. 144
6. 153
Find the GCF of each pair of numbers.
|. J 6 and 20
8. 9 and 36
9. 15 and 28
10. 35 and 42
11. 33 and 66
12. 100 and 120
^3. 78 and 30
14. 84 and 42
Find the GCF of each pair of monomials.
15. 15x4and35x2
16. 12p2 and 30g5
17. -6f 3 and9f
18. 27y3zand45x2y
19. 12atoand12
20. -3d3 and Ud4
21. -mV and 3m6n
22. ^Qgh^ and 5/7
2|. Kirstin is decorating her bedroom wall with photographs.
She has 36 photographs of family and 28 photographs of friends.
She wants to arrange the photographs in rows so that each row
has the same number of photographs, and photographs of family
and photographs of friends do not appear in the same row.
a. How many rows will there be if Kirstin puts the greatest possible
number of photographs in each row?
b. How many photographs will be in each row?
Copyright ©by Holt, Rinehart and Winston.
All rights reserved.
A
^
Hdlt
ii«n
Name
LESSON
Date
Class.
Practice C
Factors and Greatest Common Factors
Write the prime factorization of each number.
1. 75
2. 160
3. 3500
Find the GCF of each set of numbers.
4. 18 and 36
5. 54 and 60
6. 30 and 49
7. 72 and 54
8. 12, 18, and 30
9. 8, 20, and 28
10. 15, 20, and 42
11. 16, 24 and 56
Find the GCF of each set of monomials.
12. 21m3 and 28m
13. 13xand26
14. 8x2y and -12x3y2
15. 30sY and 36s3f5_
16. 18f5, 120s4, and 30f2
17. 4x2, 2x6, and -x3_
18. -6m5, 5n6, and 8n
19. 35y4z, -14y3z2, and -7y2
20. Emilio has 30 oranges, 45 apples, and 20 pears with which to
make fruit baskets. He wants each fruit basket to contain the same
number of each type of fruit. If he puts the greatest possible number
of each type of fruit into each basket, how many fruit baskets can he
make? How many pieces of each type of fruit will be in each basket?
21. Nina is babysitting a little boy who has a collection of small
vehicles. He has 36 cars, 12 vans, and 27 trucks. The boy is
trying to line up the vehicles in rows, with the same number of
vehicles in each row. He does not want different types of vehicles
to be in the same row. Describe the arrangement of the rows if Nina
helps the boy put the greatest possible number of vehicles in each row.
Copyright © by Holt, Rinehart and Winston.
All nghts reserved.
5
Holt AlQ8bf3 1
5. 24 • 32
Problem Solving
7. 4
1. x 2 - 16; $128
9. 1
11. 33
2. OJSx2 - x- 65; 2575 square feet
3.x 2 -144 in2
4. D
5. G
6. A
13. 6
15. 5X2
17. 3f
19. 12
21. m6n
23. a. 16
b. 4
7. G
Reading Strategies
1 . difference of squares
2. perfect square trinomial
3. It will have 3 terms.
4. c4 + 20c2d+100d2;
perfect square trinomial
6. 3 2 -17
8. 9
10. 7
12.
14.
16.
18.
20.
22.
20
42
6
9y
2C/3
5h
Practice C
5. 4s2 - 9; difference of squares
LESSON 8-1
1 . 3 • 52
2. 25 • 5
3. 22 • 53 • 7
4. 18
5
6.
C
7. 18
9. 4
,i
(/
11. 8
13. 13
3
15. 6s¥
17.x2
1r
4
I
8. 6
10. 1
12. 7m
14. 4xV
16. 6
18. 1
19.
20. 5 baskets; each will have 6 oranges,
9 apples, and 4 pears.
7.) I,
21. There will be 25 rows with 3 vehicles in
each row. There will be 12 rows of cars,
4 rows of vans, and 9 rows of trucks.
Review for Mastery
1-
I .)
2|44
IS)
Practice B
1. 2'32
2. 23 • 3 • 5
3. 23>7
4. 2 . 3 . 5 . 1 3
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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Holt McDougal Algebra 1