Embed Size (px)
DESCRIPTION
GOOD AFTERNOON!. Today we will be learning about Prime Factorization. Warm-Up: 1.)3 x 5 x 7 = 105 2.)2 x 2 x 2 x 3 = 24 3.)2 x 3 x 3 x 5 = 90 4.)7 x 7 x 11 = 539. Remember that when two or more numbers are multiplied, each number is called a FACTOR of the product*. - PowerPoint PPT Presentation
Citation preview
CONFIDENTIAL 1
Today we will be learning about Prime Factorization.
Warm-Up:
1.) 3 x 5 x 7 = 105
2.) 2 x 2 x 2 x 3 = 24
3.) 2 x 3 x 3 x 5 = 90
4.) 7 x 7 x 11 = 539
GOOD AFTERNOON!
CONFIDENTIAL 2
Remember that when two or more numbers are multiplied,each number is called a FACTOR of the product*.
1 x 6 = 6 and 2 x 3 = 6
1 & 6, and 2 & 3are the factors of 6
* Remember that "product" is the answer to a multiplication problem.
CONFIDENTIAL 3
1 2 3 4 6 8 12 24
We also learned how to find all the factors of a number by
RAINBOW FACTORING
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24
CONFIDENTIAL 4
COMPOSITE NUMBER - A number greater than 1 with more than two factors
Today we're going to learn how to identifyCOMPOSITE NUMBERS
andPRIME NUMBERS
Can you think of a number that we would classify as COMPOSITE?
What are its factors?Example: 28
The factors of 28 are 1 and 28, 2 and 14, and 4 and 7. since 28 has more than two factors, it is a composite number.
CONFIDENTIAL 5
PRIME NUMBERS
A Prime Number is a whole number that has exactly two factors.....
1 and itself
Can you think of a number like that?
Example: 11The factors of 11 are 1 and 11. Since there are exactly two factors, 1 and the number itself, 11 is a prime number.
CONFIDENTIAL 6
Let's try to name the first 8 prime numbers.
2 3 5 7 11 13 17 19
(Hint: The numbers 0 and 1 are neither prime nor composite. 1 has only 1 factor.0 has an infinite number of factors.
To Check
CONFIDENTIAL 7
Tell me whether each number below isPrimeCompositeNeither
(a) 28
(b) 11
(c) 48
(d) 7
(e) 81
(f) 1
Composite
Prime
Composite
Prime
Composite
Neither
CONFIDENTIAL 8
Did you know that EVERY Composite Number can beexpressed as a product of prime numbers???
This is called PRIME FACTORIZATION.
CONFIDENTIAL 9
A factor tree can be used to find the PRIME FACTORIZATION of a number.
Write the number beingfactored at the top.Choose any pair ofwhole number factors.
Continue to factor anynumber that is not prime.
Except for the order, theprime factors are the same.
54 54
3 18
3 2 9
3 2 33
x
xx
2 27
2 3 9
2 33 3 x x x
x
xx
x x x
THE PRIME FACTORIZATION OF 54 IS 2 x 3 x 3 x 3;This can be written as 2 x 33
CONFIDENTIAL 10
A factor tree can be used to find the PRIME FACTORIZATION of a number.
Your Turn!
36 60
We write the Prime Factorization in order starting with the smallest prime number.
Write the number beingfactored at the top.Choose any pair ofwhole number factors.
Continue to factor anynumber that is not prime.
Except for the order, theprime factors are the same.
2 18
2 2 9
2 32 3
x
xx
x x x
THE PRIME FACTORIZATION OF 36 IS 2 x 2 x 3 x 3;This can be written as 22 x 32
2 30
2 2 15
2 52 3
x
xx
x x x
THE PRIME FACTORIZATION OF 60 IS 2 x 2 x 3 x 5;This can be written as 22 x 3 x 5
(a) (b)
CONFIDENTIAL 11
75 42
Here are a few more you can try!
Write the number beingfactored at the top.Choose any pair ofwhole number factors.
Continue to factor anynumber that is not prime.
Except for the order, theprime factors are the same.
3 25
3 5 5
x
xx
2 21
2 3 7
x
xx
THE PRIME FACTORIZATION OF 75 IS 3 x 5 x 5;This can be written as 3 x 52
THE PRIME FACTORIZATION OF 42 IS 2 x 3 x 7
(a) (b)
CONFIDENTIAL 12
Jessica bought bags of snacks at the store and each bag cost the same price.
She spent a total of $30. Find three possible costs per bag and the number
of bags she could have purchased.
Let us Practice now!
Answer:$10 and 3 bags;$3 and 10 bags;$2 and 15 bags
CONFIDENTIAL 13
length
height
wid
th
To find the volume of a box, youcan multiply its length by its height byits width.
length x height x width
The measure of the volume of a box is 357. Find its possible dimensions.
Answer: 3 x 7 x 17
CONFIDENTIAL 14
Did you know that all odd numbers greater than 7can be expressed as the sum of 3 Prime Numbers???
Which three prime numbers have a sum of 59?
Answer: 7 + 23 +29
CONFIDENTIAL 15
1.) What is a Prime Number? Can you give me some examples?
3.) Tell whether each number is Prime, Composite, or Neither.
a. 10b. 3c. 1d. 61
4.) Write the number 38 as the product of prime numbers.
5.) Use a factor tree to find the Prime Factorization of 90.
2.) What is a Composite Number? Can you give me some examples?
A whole number that has exactly two unique factors, 1 and the number itself, is a prime number.Examples: 3, 5, 7, 11
A number greater than 1 with more than two factors, is a composite number.Examples: 6, 9, 12, 15
Composite
Prime
Neither
Prime
38 = 2 x 19
90
2 45
3 152
32 3
x
x
xx
x
The Prime Factorization of 90 is 2 x 32 x5
5x
CONFIDENTIAL 16
You worked very hard today!
Prime Number
Composite Number
Neither Prime nor Composite
A whole number that hasexactly 2 factors - 1 and itself.
A number greater than 1with more than 2 factors.
"1" has only 1 factor"0" has an infinite number of factors.
Let's review what we learned.
Examples: 3, 7, 19
Examples: 4, 12, 22
Examples: 1 and 0
CONFIDENTIAL 17
We also learned how to find the PRIME FACTORIZATIONof a number using a Factor Tree.
56
2 28
2 142
2 72 2
x
x
xxx
x
The Prime Factorization of 56 is 2 x 2 x 2 x 7
