5 Minute CheckComplete in your notebook.Find the prime factorization for each number.

1. 282. 333. 324. 102

5 Minute CheckFind the prime factorization for each number.

28 / \ 2 X 14 I / \ 2 X 2 X 7

5 Minute CheckFind the prime factorization for each number.

33

5 Minute CheckFind the prime factorization for each number.

33 / \ 3 X 11

5 Minute CheckFind the prime factorization for each number.

32

5 Minute CheckFind the prime factorization for each number.

32 / \ 2 X 16 I / \ 2 X 2 X 8 I I / \ 2 X 2 X 2 X 4

I I I / \ 2 X 2 X 2 X 2 X 2 or 2⁵

5 Minute CheckFind the prime factorization for each number.

102

5 Minute CheckFind the prime factorization for each number.

102 / \ 2 X 51 I / \ 2 X 3 X 17

Thursday, August 29

Prime Factors

Prime Factors

Every composite number can be expressed asa product of prime numbers. This is called

prime factorization of the number.

A factor tree can be used to find the primefactorization of a composite number.

Prime FactorsRemember – When constructing a factor

tree, prime numbers have one “root” and composite numbers have two “roots”.

45 / \

3 X 15 I / \

3 X 3 X 5

Prime Factors

Find the prime factorization of 36.

What do we do first?

Prime Factors

Find the prime factorization of 36.

Is 36 divisible by 2?

Prime Factors

Yes, 36 ÷ 2 = 18

36 / \ 2 X 18

We keep dividing by 2 until it is not divisible. Is 18 divisible by 2?

Prime Factors

Yes, 18 ÷ 2 = 936

/ \ 2 X 18 I / \

2 X 2 X 9

Is 9 divisible by 2?

Prime Factors

No.36

/ \ 2 X 18 I / \

2 X 2 X 9

What’s next?

Prime Factors

No.36

/ \ 2 X 18 I / \

2 X 2 X 9

Is 9 divisible by 3?

Prime FactorsYes, 9 ÷ 3 = 3 36

/ \ 2 X 18 I / \ 2 X 2 X 9 I I / \ 2 X 2 X 3 X 3

Once we have all prime numbers, we are done. The prime factorization of 36 is 2 X 2 X 3 X 3, or 2² X 3².

Prime FactorsFind the prime factorization of 88.

Do this on your own.

Prime FactorsFind the prime factorization of 88.

88 / \ 2 X 44 I / \ 2 X 2 X 22 I I / \ 2 X 2 X 2 X 11

Prime FactorsFind the prime factorization of 147.

Do this on your own.

Prime FactorsFind the prime factorization of 147.

147 / \ 3 X 49 I / \ 3 X 7 X 7

Prime Factors

Can you give an example of a whole number that is neither a prime nor composite number?

Prime Factors

Can you give an example of a whole number that is neither a prime nor composite number?

1

Prime Factors

There are 8 numbers between 2-100 that have an odd number of factors. What are they?

Prime Factors

There are 8 numbers between 2-100 that have an odd number of factors. What are they?

Hint-factor rainbows

Prime Factors

There are 8 numbers between 2-100 that have an odd number of factors. What are they?

Hint-factor rainbows

2nd hint – remember if you multiply a number by itself, it is only listed one time in a factor rainbow.

Prime Factors

There are 8 numbers between 2-100 that have an odd number of factors. What are they?

4:1,2,49:1,3,916:1,2,4,8,1625:1,5,2536:1,3,4,6,9,12,3649:1,7,4964: 1,2,4,8,16,32,62

81:1,3,9,27,81

Prime Factors

List all factors of 18.

Prime Factors

List all factors of 18.

The easiest way to list ALL factors is to create a multiples list. Notice it did not say to list the prime factors.

18: 1, 2, 3, 6, 9, 18

Prime Factors

List all prime factors of 18.

Prime FactorsList all prime factors of 18.

The easiest way to list prime factors is to create a factor tree.

18

/ \ 2 X 9 I / \

Prime Factors 2 X 3 X 3

Prime Factors

List all factors of 38.

Prime Factors

List all factors of 38.

38:1, 2, 19, 38

Prime Factors

List all prime factors of 38.

Prime Factors

List all prime factors of 38. 38

/ \Prime Factors 2 X 19

Prime Factors

List all factors of 44.

Prime Factors

List all factors of 44.

44: 1, 2, 4, 11, 22, 44

Prime Factors

List all prime factors of 44.

Prime Factors

List all prime factors of 44. 44

/ \ 2 X 22 I / \

Prime Factors 2 X 2 X 11

Prime Factors

List all factors of 144.

Prime Factors

List all factors of 144.

44: 1, 2, 3, 4, 6, 8, 12, 18, 24, 36, 48, 72, 144

Prime Factors

List all prime factors of 144.

Prime Factors

List all prime factors of 144. 144

/ \ 2 X 72 I / \

2 X 2 X 36 I I / \

2 X 2 X 2 X 18 I I I / \

2 X 2 X 2 X 2 X 9 I I I I / \

Prime Factors 2 X 2 X 2 X 2 X 3 X 3 or 2⁴ X 3²

Prime Factors

The idea that we can express any number greater than 1 as a prime

number or a product of prime numbers is called the

Fundamental Theorem of Arithmetic.

Prime Factors

Agenda Notes-Homework

Prime Factorization Worksheet #2Due 8-30-13

Quiz on Friday, Aug 30