CONFIDENTIAL 1

Today we will be learning about Prime Factorization.

Warm-Up:

1.) 3 x 5 x 7 =

2.) 2 x 2 x 2 x 3 =

3.) 2 x 3 x 3 x 5 =

4.) 7 x 7 x 11 =

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?

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?

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

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.

(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.

(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!

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.

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?

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?

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