Properties of Numbers

Multiples and Factors

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

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

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

Let’s name the first five multiples:

• 3:

• 6:

• 7:

• 4:

What are the factors of 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.

The only factors of 7 are 1,7

Find the Missing Multiples

• 6, 12, 18, ____, ____

• ___, 6, 9, 12, ____, ____, 21

• ___, 24, 36, 48, 60, ____

24 30

3 15 18

12 72

IntegersIntegers

Answer these:1. Write down the factors of:

a) 15b) 64c) 48d) 32e) 72f) 84

2. Write down the first 5 multiples ofa) 3b) 2c) 5d) 13e) 15f) 16

1, 3, 5, 151, 2, 4, 8, 16, 32, 641, 2, 3, 4, 6, 8, 12, 16, 24, 48

1, 2, 4, 8, 16, 321, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 721, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

3, 6, 9, 12, 152, 4, 6, 8, 105, 10, 15, 20, 2513, 26, 39, 52, 6515, 30, 45, 60, 7516, 32, 48, 64, 80

Lowest Common Multiple (LCM)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

8162432404856647280

142842567084

56 is the first number to appear in each list and so 56 is the LCM

LCM and HCF Harder QuestionsLCM and HCF Harder Questions

A farmer has 24 cows and 30 sheep. She decides to divide theseequally between her sons. What is the greatest number of sons she can have?

HCF question: List the factors of both:

24123468

1224

3012356

101530

Number of sons she can have is 6

Homework Time

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

Prime and Composite Numbers

Prime numbers are numbers that only have two factors: one, and the number itself.

EXAMPLES:

3, 5, 7, 11, 31

Composite numbers

have more than two

factors.

EXAMPLES:

6, 18, 30, 100

Which list contains all prime numbers?

A. 1, 2, 3, 7

B. 2, 3, 7, 13

C. 11, 13, 9, 17

D. 21, 23, 37, 41

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?

Guiding Question

• How are multiples different from factors?

• 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?

What do you think?Discussion

Let’s Review our Guiding Questions

• What are multiples?

• How are multiples different from factors?

Take a few minutes to answer these in your journal.

Journal Time

• 1, 6, 20, 2, 12, 3, 4, 9, 16, 5, 11, 28, 25From 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