5 Minute Check Complete in your notebook. Find the prime factorization for each number. 28 33 32 102

5 Minute Check Find the prime factorization for each number. 28 / \ 2 X 14 I / \ 2 X 2 X 7

5 Minute Check Find the prime factorization for each number. 33

5 Minute Check Find the prime factorization for each number. 33 / \ 3 X 11

5 Minute Check Find the prime factorization for each number. 32

5 Minute Check / \ 2 X 16 I / \ 2 X 2 X 8 I I / \ 2 X 2 X 2 X 4 Find 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 Check Find the prime factorization for each number. 102

5 Minute Check Find 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 as a product of prime numbers. This is called prime factorization of the number. A factor tree can be used to find the prime factorization of a composite number.

Prime Factors Remember – 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 = 9 36 / \ 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 Factors Yes, 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 Factors Find the prime factorization of 88. Do this on your own.

Prime Factors Find 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 Factors Find the prime factorization of 147. Do this on your own.

Prime Factors Find 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? 4:1,2,4 9:1,3,9 16:1,2,4,8,16 25:1,5,25 36:1,3,4,6,9,12,36 49:1,7,49 64: 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 Factors List 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 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 #2 Due 8-30-13 Quiz on Friday, Aug 30