2. 5 Minute Check Complete in your notebook.
Find the prime factorization for each number. 28 33 32
102

3. 5 Minute Check
Find the prime factorization for each number. 28
/ \
2 X 14
I / \
2 X 2 X 7

4. 5 Minute Check
Find the prime factorization for each number. 33

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

6. 5 Minute Check
Find the prime factorization for each number. 32

7. 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

8. 5 Minute Check
Find the prime factorization for each number. 102

9. 5 Minute Check
Find the prime factorization for each number.
102
/ \
2 X 51
I / \
2 X 3 X 17

10. Thursday, August 29
Prime Factors

11. 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.

12. 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

13. Prime Factors
Find the prime factorization of 36.
What do we do first?

14. Prime Factors
Find the prime factorization of 36. Is 36 divisible by 2?

15. Prime Factors
Yes, 36 ÷ 2 = / \ 2 X 18 We keep dividing by 2 until it is not divisible. Is 18 divisible by 2?

16. Prime Factors
Yes, 18 ÷ 2 = 9 36 / \ 2 X 18 I / \ 2 X 2 X 9 Is 9 divisible by 2?

17. Prime Factors
No. 36 / \ 2 X 18 I / \ 2 X 2 X 9 What’s next?

18. Prime Factors
No. 36 / \ 2 X 18 I / \ 2 X 2 X 9 Is 9 divisible by 3?

19. 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.

20. Prime Factors
Find the prime factorization of 88. Do this on your own.

21. Prime Factors
Find the prime factorization of / \ 2 X 44 I / \ 2 X 2 X 22 I I / \ 2 X 2 X 2 X 11

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

23. Prime Factors
Find the prime factorization of / \ 3 X 49 I / \ 3 X 7 X 7

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

25. Prime Factors
Can you give an example of a whole number that is neither a prime nor composite number? 1

26. Prime Factors
There are 8 numbers between that have an odd number of factors. What are they?

27. Prime Factors
There are 8 numbers between that have an odd number of factors. What are they? Hint-factor rainbows

28. Prime Factors
There are 8 numbers between 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.

29. Prime Factors
There are 8 numbers between 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

30. Prime Factors
List all factors of 18.

31. 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

32. Prime Factors
List all prime factors of 18.

33. 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 X 3 X 3

34. Prime Factors
List all factors of 38.

35. Prime Factors
List all factors of :1, 2, 19, 38

36. Prime Factors
List all prime factors of 38.

37. Prime Factors
List all prime factors of / \ Prime Factors 2 X 19

38. Prime Factors
List all factors of 44.

39. Prime Factors
List all factors of : 1, 2, 4, 11, 22, 44

40. Prime Factors
List all prime factors of 44.

41. Prime Factors
List all prime factors of / \ 2 X 22 I / \ Prime Factors 2 X 2 X 11

42. Prime Factors
List all factors of 144.

43. Prime Factors
List all factors of : 1, 2, 3, 4, 6, 8, 12, 18, 24, 36, 48, 72, 144

44. Prime Factors
List all prime factors of 144.

45. 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 X 2 X 2 X 2 X 3 X 3 or 2⁴ X 3²

46. 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.

47. Prime Factors
Agenda Notes- Homework Prime Factorization Worksheet #2 Due Quiz on Friday, Aug 30