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Name:__________________________________________ Date:_____________________ Period:_____
DIAMOND PROBLEMS #1
Complete the problems below (remember, the product goes on the top & the sum goes on the bottom)
EX.
1.
2.
3.
a*b
a
b
3
5
4
!7
7
!5
!8
1
a+b
4.
5.
5
!7
8.
6.
1
!6
9.
7.
2
10.
11.
21
0
9
12.
!32
!7
14.
81
!7
!56
4
7
13.
63
3
15.
!18
9
6
3
7
ALGEBRA 1 – UNIT 14 · FACTORING: NOTES & PRACTICE
PAGE 2
Name:__________________________________________ Date:_____________________ Period:_____
DIAMOND PROBLEMS #2
Complete the problems below (remember, the product goes on the top & the sum goes on the bottom)
EX.
16.
17.
18.
14
a*b
a
b
!2
a+b
19.
!7
!5
20.
!5
21.
!9
22.
!10
!30
4
!25
3
1
5
0
23.
24.
25.
26.
!42
16
!49
!36
!1
8
0
0
27.
28.
29.
30.
90
90
55
12
19
!23
!16
!7
ALGEBRA 1 – UNIT 14 · FACTORING: NOTES & PRACTICE
PAGE 3
Name:__________________________________________ Date:_____________________ Period:_____
FIND THE GREATEST COMMON FACTOR (GCF)
Find the GCF of each set of numbers or monomials.
Greatest Common Factor
The greatest of the factors common to two or more numbers is called the
greatest common factor (GCF) of the numbers. One way to find the GCF
is to list the factors of the numbers.
1. 48, 16
Find the GCF
1 Find the greatest common factor of 36 and 60.
METHOD 1
2. 8, 28
List the factors.
factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Common factors of
36 and 60: 1, 2, 3, 4, 6, 12
The greatest common factor of 36 and 60 is 12.
METHOD 2
Use prime factorization.
36 = 2 · 2 · 3 · 3
Common prime factors of
36 and 60: 2, 2, 3
60 = 2 · 2 · 3 · 5
3. 32y, 32
The GCF is 2 · 2 · 3 or 12.
Find the GCF
2 Find the greatest common factor of 54, 81, and 90.
Use a factor tree to find the prime factorization of each number.
54
81
90
6 · 9
9 · 9
9 · 10
2 · 3 · 3 · 3
3 · 3 · 3 · 3
3 · 3 · 2 · 5
4. 12! ! , 24! !
The common prime factors of 54, 81, and 90 are 3 and 3.
The GCF of 54, 81, and 90 is 3 · 3 or 9.
5. 32mn2, 32n2
9. 24yx2, 32x2, 16x2
6. 49x2, 28x3
7. 27n2m, 36m3
8. 43x, 3x2
10. 50y2, 20x2, 70y
ALGEBRA 1 – UNIT 14 · FACTORING: NOTES & PRACTICE
PAGE 5