1. Properties of Numbers
Need white copy paper for double bubbles.

2. Multiples and Factors

3. Learning Goals
Identify prime, composite, square, even and odd numbers.
Determine if one number is a factor or a multiple of another number
Identify and learn multiplication combinations

4. Factors
Factors are the numbers you multiply together to get a product.
For example, the product 24 has several factors.
24 = 1 x 24
24 = 2 x 12
24 = 3 x 8
24 = 4 x 6
SO, the factors are 1, 2, 3, 4, 6, 8, 12, 24

5. Multiples
A multiple is formed by multiplying a given number by the counting numbers.
The counting numbers are 1, 2, 3, 4, 5, 6, etc.

6. 4 × 5 = 20
Factors
Multiple

7. Let’s name the first five multiples:3: 6: 7: 4:
GLASS MODE

8. What are the factors of 7?
The only factors of 7 are 1,7
1 x 7
2 x ??
3 x ??
4 x ??
5 x ??
6 x ??
7 x 1
This works, but it is a repeat. We are done.

9. Find the Missing Multiples24 30
6, 12, 18, ____, ____
___, 6, 9, 12, ____, ____, 21
___, 24, 36, 48, 60, ____ 15 18 3 72 12

10. Integers
Answer these:
Write down the factors of:
a) 15
b) 64
c) 48
d) 32
e) 72
f) 84
2. Write down the first 5 multiples of
a) 3
b) 2
c) 5
d) 13
e) 15
f) 16
1, 3, 5, 15
1, 2, 4, 8, 16, 32, 64
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
1, 2, 4, 8, 16, 32
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
3, 6, 9, 12, 15
2, 4, 6, 8, 10
5, 10, 15, 20, 25
13, 26, 39, 52, 65
15, 30, 45, 60, 75
16, 32, 48, 64, 80

11. Lowest Common Multiple (LCM)
To find the lowest common multiple of two numbers,
simply list the multiple of each number and the first number that
appears in both lists is the LCM.
e.g. Find the LCM of 8 and 14 8 16 24 32 40 48 56 64 72 80 14 28 42 56 70 84
56 is the first number to appear
in each list and so 56 is the LCM

12. LCM and HCF Harder Questions
A farmer has 24 cows and 30 sheep. She decides to divide these
equally between her sons.
What is the greatest number of sons she can have?
HCF question:
List the factors of both: 24 1 2 3 4 6 8 12 30 1 2 3 5 6 10 15
Number of sons she can have is 6

13. Homework Time
Math Makes Sense Textbook – pg 44; Q’s 1, 2, 5, 8

14. Prime and Composite Numbers
have more than two
factors.
EXAMPLES:
6, 18, 30, 100
Prime numbers are
numbers that only have
two factors: one, and the
number itself.
EXAMPLES:
3, 5, 7, 11, 31

15. Which list contains all prime numbers?
1, 2, 3, 7
2, 3, 7, 13
11, 13, 9, 17
21, 23, 37, 41
GLASS MODE

16. Let’s review what we’ve learned
How can you know if a number is a prime number?
How can an array help you identify a square number?
What is a factor?
What is a strategy you can use to find all the factors of a given number?
Glass mode: Who can write an equation for this array? Who can write it with more than 2 factors?

17. Guiding Question
How are multiples different from factors?

18. Discussion
What do you think?
Did you find any “favorite” strategy that helped you, that you could share with the rest of us?
Which ones did you find most
challenging?
Did any of your puzzles have more than
one answer? Or no answer?

19. Let’s Review our Guiding Questions
What are multiples?
How are multiples different from factors?
Share
Take a few minutes to answer these in your journal.

20. Journal Time
1, 6, 20, 2, 12, 3, 4, 9, 16, 5, 11, 28, 25
From this list of numbers, write down:
The prime numbers
The multiples of 4
The factors of 6
Square Numbers
(You might use some numbers more than once)
Complete the Number Line handout for factors & multiples