# Greatest Common Factor

```Do Now 2/8/11
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Take out HW from Friday.
 Text
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page 179, #12-27 all, &amp; 32
 Text
page 179, #28-31 all, 33, 37-45 all
 Quiz sections 4.1 &amp; 4.2 Wednesday.
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In your journal, explain why a single number does
not have a GCF. Then find the GCF of 96 and 54.
Homework
Text page 179, #12-27 all, &amp; 32
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12) 14
13) 3
14) 17
15) 12
16) 1
17) 1
18) 2
19) 120
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20) 1; relatively prime
21) 11; not relatively prime
22) 3; not relatively prime
23) 1; relatively prime
24) 2; not relatively prime
25) 1; relatively prime
26) 16; not relatively prime
27) 28; not relatively prime
32) 8 bands; 4 vocalists
Objective
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SWBAT find the greatest common factor of
two or more whole numbers
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SWBAT find the greatest common factor of
two or more monomials
Section 4.2 “Greatest Common Factor”
Greatest Common Factor
The LARGEST common factor of two numbers.
Find the GCF of 8 and 12.
List the factors of the two numbers and then compare.
8: 1, 2, 4, 8
12: 1, 2, 3, 4, 6, 12
From the list you can see that 1, 2, and 4 are common factors.
Of these 4 is the greatest common factor.
Greatest Common Factors
Find the GCF of 180 and 378.
When the numbers are too large to list the factors
of the two numbers, find the prime factorization of each
and then compare.
180: 2 &middot; 2 &middot; 3 &middot; 3 &middot; 5
378: 2 &middot; 3 &middot; 3 &middot; 3 &middot; 7
From the list you can see that 2, 3, and 3 are common prime
factors. The greatest common factor of 180 and 378 is the
product of 2 &middot; 3 &middot; 3 which is 18.
Greatest Common Factors
Find the GCF of 39 and 50.
When the numbers are too large to list the factors
of the two numbers, find the prime factorization of each
and then compare.
39: 3 &middot; 13
50: 2 &middot; 5 &middot; 5
Relatively Prime:
Two numbers are relatively
prime if their greatest common
factor is 1.
From the list you can see that there are NO common prime
factors. However, two numbers always have 1 as a common
factor. So the GCF is 1 and the two numbers are relatively
prime.
GCF of Variable Expressions
Find the GCF of 12x&sup2;y and 6xy&sup3;.
Write the prime factorization of each and then compare.
12x&sup2;y:
2&middot;2&middot;3&middot;x&middot;x&middot;y
6xy&sup3;:
2&middot;3&middot;x&middot;y&middot;y&middot;y
From the list you can see that 2, 3, x, and y are common prime
factors. The greatest common factor is the
product of 2 &middot; 3 &middot; x &middot; y, which is 6xy.
GCF of Variable Expressions
Find the GCF of 18xy&sup2; and 28x&sup2;y&sup3;.
Write the prime factorization of each and then compare.
18xy&sup2;:
2&middot;3&middot;3&middot;x&middot;y&middot;y
28x&sup2;y&sup3;:
2&middot;2&middot;7&middot;x&middot;x&middot;y&middot;y&middot;y
From the list you can see that 2, x, y, and y are common prime
factors. The greatest common factor is the
product of 2 &middot; x &middot; y &middot; y, which is 2xy&sup2;.
Greatest Common Factors
Find the GCF of 12x&sup2;y, 18xy&sup3;, and 30x&sup2;y&sup3;.
List the factors of the three numbers and then compare.
12x&sup2;y:
2&middot;2&middot;3&middot;x&middot;x&middot;y
18xy&sup3;:
2&middot;3&middot;3&middot;x&middot;y&middot;y&middot;y
30x&sup2;y&sup3;: 2 &middot; 3 &middot; 5 &middot; x &middot; x &middot; y &middot; y &middot; y
From the list you can see that 2, 3, x, and y are common prime
factors. The greatest common factor is the
product of 2 &middot; 3 &middot; x &middot; y, which is 6xy.
Greatest Common Factors
Find the GCF of 48a&sup2;b, 64ab&sup3;, and 80a&sup2;b&sup3;.
48a&sup2;b :
2&middot;2&middot;2&middot;2&middot;3&middot;a&middot;a&middot;b
64ab&sup3; :
2&middot;2&middot;2&middot;2&middot;2&middot;2&middot;a&middot;b&middot;b&middot;b
80a&sup2;b&sup3; : 2 &middot; 2 &middot; 2 &middot; 2 &middot; 5 &middot; a &middot; a &middot; b &middot; b &middot; b
From the list you can see that 2, 2, 2, 2, a, and b are common
prime factors. The greatest common factor is the
product of 2 &middot; 2 &middot; 2 &middot; 2 &middot; a &middot; b which is 16ab.
24
Homework
 Text
page 179, #28-31 all, 33, 37-45 all
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