Bell Work: Rules of Membership

1
Bell Work Rules of Membership

• What are the rules that allow a prime number to
  be a prime number?
• What are the rules that allow a composite number
  to be a composite number?
• Sort the following numbers into groups according
  to your rules of membership.
• Explain why you put them there.
• Did any numbers not fit? Why?

• 0
• 1
• 5
• 12
• 18
• 19

37 61 73 87 99 100
2
Review of Yesterdays Material

• Prime v. Composite
• Divisibility Rules
• Prime Factorization

3
Mrs. ORegans Rules of Membership
PRIME NUMBERS
COMPOSITE NUMBERS
DOES NOT BELONG
1
0
12
5
15
61
19
73
37
87
99
100
4
Prime number Prime number What do you see? I see
no other factors Except for one and
me. Composite number Composite number What do
you see? I see at least three factors Including
one and me.
5
Divisibility Rules
Use the rules we learned yesterday to determine
whether or not these two numbers are divisible by
the factors below it.

• 396
• 2
• 3
• 4
• 5
• 6
• 7
• 9
• 10

• 7935
• 2
• 3
• 4
• 5
• 6
• 7
• 9
• 10

yes
no
Its an even number
Its an odd number
yes
yes
3 9 6 18 ? 18 3 6
7 9 3 5 24 ? 24 3 8
yes
96 4 24
no
35 4 does not divide evenly
no
It does not end in a 5
yes
It ends in a 5 or a zero
yes
The rules for 2 and 3 work
no
The rule for 2 does not work
no
7 x 2 14 ? 39 14 25 ? 25 is not divisible
by 7
no
5 x 2 10 ? 793 10 783 ? 783 is not
divisible by 7
yes
3 9 6 18 ? 18 9 2
7 9 3 5 24 ? 24 is not divisible by 9
no
no
It does not end in a 0
no
It does not end in a 0
6
Yesterdays Challenge Problem

• Use what you know about multiplying whole numbers
  by variables and exponents to make a factor tree
  for the following monomial
• 45x3

32 ? 5 ? x3
x3
45
9
x
x
x
5
3
3
7
Greatest Common Factor

• Lesson 4-4

8
Todays Math Standard

• Number Sense 2.4
• Determine the least common multiple and the
  greatest common divisor of whole numbers use
  them to solve problems with fractions (e.g., to
  find a common denominator to add two fractions or
  to find the reduced form for a fraction).

9
Key Vocabulary

• Greatest
• biggest
• Common
• shared
• Factor
• One of the numbers multiplied to get a product
• Factor Factor Product

10
The Greatest Common Factor (GCF)is also known as
theGreatest Common Divisor (GCD)
Factor Factor Product
11
Steps to finding the GCF

• Make a factor tree for each of the numbers
• Write out the prime factorization of each number
• Write the factors from least to greatest
• Make a Venn diagram
• Place the exponents in the correct part of the
  Venn
• Look at the overlap area of the Venn diagram
• If there are no factors, then the GCF is 1
• If there is one factor, then that is the GCF
• If there is more than one factor, then multiply
  all the factors together

12
What is the GCF of 28 and 32?
13
Make a factor tree for each of the numbers.
28
32
14
2
16
2
8
2
2
7
4
2
2
2
14
Write out the prime factorization of each number
28
32
14
2
16
2
8
2
2
7
4
2
28 2 2 7
32 2 2 2 2 2
2
2
15
Make a Venn diagram.
28 22 7
32 25
28 2 2 7
32 2 2 2 2 2
16
Make a Venn diagram.
28 2 2 7
32 2 2 2 2 2
28 and 32 have two 2s in common.
32 has three more 2s than 28.
28 has a factor of 7, but 32 does not.
2
2
2
2
7
2
17
Look at the overlap area of the Venn diagram
Common factors 28 and 32 share two 2s
2
2
2
2
7
2
GREATEST (biggest) COMMON FACTOR Multiply the
common factors together. 2 2 4
18
What is the GCF of 28 and 32?

• The GCF is 4.

19
Put this next one on your notes page.
20
What is the GCF of 60 and 45?
21
Make a factor tree for each of the numbers.
60
45
10
6
9
5
3
3
2
5
2
3
22
Write out the prime factorization of each number
60
45
10
6
9
5
3
3
2
5
2
3
60 2 2 3 5
45 3 3 5
23
Make a Venn diagram.
60 22 3 5
45 32 5
60 2 2 3 5
45 3 3 5
24
Make a Venn diagram.
60 2 2 3 5
45 3 3 5
60 and 45 have a 3 and a 5 in common.
45 has another 3 for a factor, but 60 does not.
60 has a two factors of 2, but 45 does not.
3
2
5
3
2
25
Look at the overlap area of the Venn diagram
Common factors 60 and 45 share a 3 and a 5.
60
45
3
2
5
3
2
GREATEST (biggest) COMMON FACTOR Multiply the
common factors together. 3 5 15
26
What is the GCF of 60 and 45?

• The GCF is 15.

27
Lets Practice
28
What is the GCF of 56 and 81?
29
Make a factor tree for each of the numbers.
56
81
9
9
8
7
3
3
3
3
2
4
2
2
30
Write out the prime factorization of each number
56
81
9
9
8
7
3
3
3
3
2
4
2
2
56 2 2 2 7
81 3 3 3 3
31
Make a Venn diagram.
56 23 7
81 34
56 2 2 2 7
81 3 3 3 3
32
Make a Venn diagram.
56 2 2 2 7
81 3 3 3 3
60 and 45 appear to have no factors in common!
56
81
2
3
2
3
2
3
7
3
33
Look at the overlap area of the Venn diagram
Common factors If the overlap is empty, then
the factors must recognize the ONLY factor that
every non-zero number has in common
56
81
2
3
2
3
2
3
7
3
GREATEST (biggest) COMMON FACTOR 1
34
What is the GCF of 56 and 81?

• The GCF is 1.

NOTE You will NEVER have a GCF of zero!
35
What is the GCF of 39 and 52?
36
Make a factor tree for each of the numbers.
39
52
2
26
13
3
2
13
37
Write out the prime factorization of each number
39
52
2
26
13
3
2
13
39 3 13
81 2 2 13
38
Make a Venn diagram.
39 3 13
52 22 13
39 3 13
52 2 2 13
39
Make a Venn diagram.
39 3 13
52 2 2 13
39 and 52 have the factor 13 in common!
39
52
2
13
3
2
40
Look at the overlap area of the Venn diagram
39
52
2
13
3
2
GREATEST (biggest) COMMON FACTOR 13
41
What is the GCF of 39 and 52?

• The GCF is 13.

42
What is the GCF of 45 and 76?

• The GCF is 1.

43
What is the GCF of 86 and 154?

• The GCF is 2.

44
Tonights Challenge Problem

• Find the GCF for the following monomials
• 15xy2
• 45x3y