Multiples and Factors

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.

Example: List the multiples of 4:

• 4 x 1 = 4

• 4 x 2 = 8

• 4 x 3 = 12

• 4 x 4 = 16

• 4 x 5 = 20

• 4 x 6 = 24

Counting Numbers

So, the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, etc.

What are the first five multiples of 13?

13 x 1 =13

13 x 2 = 26

13 x 3 = 39

13 x 4 = 52

13 x 5 = 65

13, 26, 39, 52, 65

Find the Missing Multiples

• 6, 12, 18, ____, ____

• ___, 6, 9, 12, ____, ____, 21

• ___, 24, 36, 48, 60, ____

24 30

3 15 18

12 72

MENTAL MATH

• Find the first 5 multiples of the following numbers

• a) 4 ____, _____, _____, _____, ____

• b) 5 ____, _____, _____, _____, ____

• c) 8 ____, _____, _____, _____, ____

• d) 15 ____, _____, _____, _____, ____

• e) 20 ____, _____, _____, _____, ____

REMEMBER! • 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

• The factors are 1, 2, 3, 4, 6, 8, 12, 24

Decomposing Factors

1. Factor Tree

2. Break the numbers down into the primefactors that make them up.

Step 1 Write the number you are going to break down

90Step 2 Plot a vertical line at the right side of

the number

90

Step 3 Write the smallest prime that divides the number. Start with number 2 and

continue with 3, 5 and son on.

• Half of 90 is 45

• 90 divided by 2 is 45

90 245

Can you divide 45 by 2 with no remainder?

•90 2 45 3 15 3 5

• Continue with the next prime number that is 3.

•90 2 45 3 15 3 5 5 1

• Continue with the next prime number that is 5.

Step 4 Repeat the same procedure until the quotient is 1

Let´s try together

120 2 Write the smallest prime

that divides the number. Start with number 2.

HALF OF 120

Let´s try together

120 260

What is the smallest prime that divides 60?

Let´s try together120 2 60 2 30

What is the smallest prime that divides 30?

HALF OF 30

Let´s try together120 2 60 2 30 2 15

What is the smallest prime that divides 15?

HALF OF 15 WITH NO REMAINDER?

Let´s try together120 2 60 2 30 2 15 3 5

What is the smallest prime that divides 5?

What is the next prime number?

Let´s try together120 2 60 2 30 2 15 3 5 5 1

HOW DO YOU EXPRESS IT?

• 2 X 2 X 2 X 3 X 5 = 120

• 2 X 3 X 5

HELP YOUR TEACHER!!

72

60

TIME TO PRACTICE

Break the following numbers down

45 126 28

Break the following numbers down

20 27 45 20 27 45