1. Prime Factorization
2-1

2.
Brainpop - Factoring video .. Answer the questions

3.
Answers: C D B A

4. Divisible
When a number can be divided by a second number and have a remainder of zero.
8 / 4 = 2
18 / 9 = 2
81 / 9 = 9

5. Divisibility Rules

6. 76 93 52 98 100 The Rule for 2 Divisibility Rules
If a number is even, then it is divisible by two.
An even number is any number that ends in a 2, 4, 6, 8, or 0
Divisibility Rules 76 93 52 98
100

7. 28 981 63 21 762 The Rule for 3 Add up all the digits.
If the sum of all digits is divisible by 3, then the whole number is divisible by 3!
6321 = =12
3 goes into 12 evenly, so 6321 is divisible by 3 28
981 63 21
762

8. The Rule for 4
The last two numbers are either 00 or they are divisible by 4.
An even number is any number that ends in a 2, 4, 6, 8, or 0
804
217
724
916
600

9. The Rule for 5
The number ends in a 5 or a zero. 93 90 75 55
100

10. The Rule for 6
If divisible by 2 and 3. 93 90 75 55
100

11. 1125 414 882 312 81 The Rule for 9 Add up all the digits.
If the sum of all digits is divisible by 9, then the whole number is divisible by 9!
6327 = =18
9 goes into 18 evenly, so 6327 is divisible by 9
1125
414
882
312 81

12. The Rule for 10
The number ends in a zero
9003
5840
6430
1020 70

13. Interactive Divisibility Rules Practice
Let’s Practice…
Interactive Divisibility Rules Practice

14. The numbers that are multiplied to get a product
Factor
The numbers that are multiplied to get a product
15 = 3 x 5
3 and 5 are factors of 15
2 x 9 = 18
2 & 9 are factors of 18
3 x 2 =6
3 & 2 are factors of 6

15. Prime Number 7 is a prime 5 is a prime
is a counting number that only has two factors, itself and one.
One is not a prime
7 is a prime
5 is a prime

16. Composite Number 8 is a composite 55 is a composite
Numbers which have more than two factors (such as six, whose factors are 1, 2, 3 and 6)
One is not a composite
8 is a composite
55 is a composite

17. A Rhyme to Help Us Remember
Prime number
What do you see?
I see no other factors
Except for one and me.
Composite number
I see at least three factors
Including one and me.

18. All of the orange numbers on this chart are prime. Write them down
All of the orange numbers on this chart are prime. Write them down. Refer to them so you don’t waste time trying to factor them. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
100

19. Prime Factorization
When a composite number is written as a product of all of its prime factors
Using the Factor Tree 78
/ \
/ \
2 x 39
/ / \
/ / \
2 x x 13

20. Let’s Try a Factor Tree! 84 / \ 2 x 42 / / \ 2 x 2 x 21 / / / \
/ \
2 x 42
/ / \
2 x x 21
/ / / \
2 x x 7

21. Factor Trees do not look the same for the same number, but the final answer is the same.72
/ \
8 x 9
/ \ / \
2 x 4 x 3 x 3
/ \
2 x 2 x 2 x 3 x 3 72
/ \
2 x 36
/ / \
2 x 2 x 18
/ / / \
2 x 2 x 2 x 9
/ / / / \
2 x 2 x 2 x 3 x 3

22. Greatest Common Factor
The largest common factor of 2 or more numbers
Use prime factorization or ladder to find GCF
GCF of 36 and 24
Is 12
GCF of 72 and 84
Is 12

23. Prime Factorization is helpful for finding greatest common factors.72
/ \
8 x 9
/ \ / \
2 x 4 x 3 x 3
/ \
2 x 2 x 2 x 3 x 3
Take the common prime factors of each number and multiply to find the greatest common factor. 84
/ \
2 x 42
/ / \
2 x x 21
/ / / \
2 x x 7
2 x 2 x 3 = 12

24. 2 72 84 2 36 42 3 18 21 6 7 Use the Ladder for LCM, GCF
and Simplifying Fractions 2 72 84
 WRITE the two numbers on one line. 2 36 42
 DRAW THE L SHAPE 3 18 21
 DIVIDE out common prime numbers starting with the smallest 6 7
LCM = 2  2  3  6  7 = 504
 LCM makes an L:
GCF is down the left side:
GCF = 2  2  3 = 12 84 72 = 7 6
Simplified fraction is on the bottom

25. 2 24 36 2 12 18 3 6 9 2 3 Use the Ladder for LCM, GCF
and Simplifying Fractions
 WRITE the two numbers on one line. 2 24 36 2 12 18
 DRAW THE L SHAPE
 DIVIDE out common prime numbers starting with the smallest 3 6 9 2 3
 LCM makes an L:
LCM = 2  2  3  2  3 = 72
GCF is down the left side:
GCF = 2  2  3 = 12 36 24 = 3 2
Simplified fraction is on the bottom

26. 1 11 13 11 13 Use the Ladder for LCM, GCF and Simplifying Fractions
 WRITE the two numbers on one line. 1 11 13 11 13
 DRAW THE L SHAPE
 DIVIDE out common prime numbers starting with the smallest
 LCM makes an L:
LCM = 11  13 = 163
GCF is down the left side:
GCF = 1
Simplified fraction is on the bottom

27. HOMEWORK PG 55 8 – 38 evens 24 – 30 use ladder method to find GCF
32 – 38 use prime factorization to find GCF (trees)

28. Resources Brain Pop – Prime Factors Brain Pop - Prime Numbers
Brain Pop - Exponents

29. Interactive Practice for Factor Trees
Virtual Manipulatives
Interactive Practice 1
Interactive Practice from MathPlayground.com

30. The Birthday Cake Method a.k.a. The Box Method
An alternative to factor trees
A video from YouTube

31. Challenge Problem
Use what you know about multiplying whole numbers by variables and exponents to make a factor tree for the following monomial
45x3 x3 45 9 5 x x x 3 3

32. A Random Thought about Prime Numbers
Brought to you from YouTube.com

33. 2 24 36 2 12 18 3 6 9 2 3 Use the Ladder for LCM, GCF
and Simplifying Fractions
 WRITE the two numbers on one line. 2 24 36 2 12 18
 DRAW THE L SHAPE
 DIVIDE out common prime numbers starting with the smallest 3 6 9 2 3
 LCM makes an L:
LCM = 2  2  3  2  3 = 72
GCF is down the left side:
GCF = 2  2  3 = 12 36 24 = 3 2
Simplified fraction is on the bottom