Page 869 - Algebra 1

Greatest Common Factor (GCF)
Skills Bank Lesson 9
The greatest common factor, or GCF, is the largest factor two or more given numbers have in common. For example, 2 and 5 are common factors of 10 and 20, but 5 is the greatest common factor.
One way to find the GCF is to make a list of factors and choose the greatest factor that appears in each list. Another way is to divide by prime factors.
Example
1
Finding the GCF
a. Find the GCF of 24 and 60. SOLUTION
24: 1, 2, 3, 4, 6, 8, 12, 24
60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 2, 3, 4, 6, and 12 are common factors. The GCF of 24 and 60 is 12.
b. Find the GCF of 54 and 72. SOLUTION
List the factors of each number. Find the greatest common factor.
2 54 72
3 27 36
3 9 12
Divide both numbers by the same prime factor.
Keep dividing until there is no prime factor that divides into both numbers without a remainder.
34
2·3·3or2·32 =18
The GCF of 54 and 72 is 18.
Using the GCF to Simplify Fractions
Example
2
a. Write _21 in simplest form. 28
SOLUTION Divide 21 and 28 by
b. Write 1_9 in simplest form. 12
t h e G C_
__
F, 7. 21÷7 _3
_ 12 12÷3 4
12 4
c. 21 and 56
g. 4, 22, and 40
_2 1 = = 28 28 ÷ 7
== 1_9 =1_3
4
Skills Bank Practice
Find the GCF.
a. 72 and 60 b. 54 and 89
e. 3, 6, and 12 f. 7, 21, and 49
Write each fraction in simplest form.
d. 120 and 960 h. 20, 45, and 80
SOLUTION Divide 9 and 12 by the GCF, 3. 99÷33
_____ i. 8 j. 15 k. 16 l. 110 m. 52 12 25 64 150 65
854 Saxon Algebra 1