Use the beans to find factors of 24 Count out 24 beans We know that products can be illustrated using a rectangular model Make a rectangle using the beans What are the numbers you multiply to get 24 ID: 559765
Download Presentation The PPT/PDF document "Finding factors of a number" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Finding factors of a number
Use the beans to find factors of 24
Count out 24 beans
We know that products can be illustrated using a rectangular model
Make a rectangle using the beans
What are the numbers you multiply to get 24?
Can you arrange the beans into a different rectangle?
What product does this represent?Slide2
How many different rectangles can you make?
Count out 11 beans.
How many rectangles can you make with 11 beans?Slide3
Sieve of Eratosthenes
Eratosthenes
was born in Cyrene which is now in Libya in North Africa in 276 BC. He died in 194 BC.
Eratosthenes made a surprisingly accurate measurement of the circumference of the Earth.
He was also fascinated with number theory, and he developed the idea of a sieve to illustrate prime numbers.Slide4
The Sieve of Eratosthenes
Prime Number
Divisible only by 1 and itself
Finding prime numbers using the sieveSlide5
Sieve of Eratosthenes
You will need many different colors. Use one color for each factor.
Circle the number “1”. 1 is neither prime nor composite, as we have seen earlier.
Now, circle 2. Every multiple of 2 is a composite number, so put a dot of that color next to all of the multiples of 2.
Use a new color. Now, circle 3. Every multiple of 3 is a composite number, so put a dot of this new color next to all multiples of 3.Slide6
Sieve of Eratosthenes
Now, 4 has a dot next to it--it is not prime. Skip it and move on.
Use a new color. Circle 5, and then put a dot of this new color next to all multiples of 5.
Now, 6 has a dot next to it--it is not prime. Skip it and move on.
Continue until you know that only prime numbers are left. When can you stop? How do you know? Slide7
Sieve of Eratosthenes
Questions to answer:
When you circled 11, were there any multiples of 11 that did not already have dots next to them?
Can you explain to a child why this was true?
What does this have to do with factors and multiples?
What are the prime numbers that are between 1 and 100?
Is 1 a prime number?Slide8
Sieve of Eratosthenes
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100Slide9
Sieve of ErathosthenesSlide10
Names for these numbers
11 is an example of a
24 is an example of aSlide11
Factors of 24
List
How should they be ordered?
How do you know you have them all?Slide12
Factors of 24--How do we know when we have them all?
1 • 12
2 • 24
3 • 8
4 • 6Slide13
Exploration 4.2
First, fill in the table on page 85, using the information on the sieve. It will help if you write them in pairs. For example, for 18: 1, 18; 2, 9; 3, 6. The order does not matter.
Next, fill in the table on page 87. Use the table on page 85 to help.Slide14
Find all of the factors of 30Slide15
Now find all of the factors of 60Slide16
Factorization
Factorization is writing a number as a product of factors.
24
60Slide17
Prime Factorization
A factorization of the number in which all of the factors are prime numbers.
10
12Slide18
Prime Factorization
24
25Slide19
Prime Factorization
Using
a factor tree to do prime
factorization.
60Slide20
112Slide21
Exploration 4.3 is due on Thursday
#1,2,6,7,8 along with some exercises from the textbook.
Please put the exploration on a separate paper than the textbook problems.