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Factors

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Factors

Factors

Example :Find the factors of 56.

Numbers that divide into 56 without leaving a remainder

F56 =1 and 56

2 and 28

4 and 14

7 and 8

Factors

Factors

Example :Find the factors of 64.

Numbers that divide into 64 without leaving a remainder

F64 =1 and 64

2 and 32

4 and 16

8 and 8

Factors

Factors

Example :Find the factors of 24.

Numbers that divide into 24 without leaving a remainder

F24 =1 and 24

2 and 12

3 and 18

4 and 6

Highest Common Factor

Highest

Common

Factor

Largest

Same

Number

We need to write out all factor pairs in order to find

the Highest Common Factor.

Highest Common Factor

Example :Find the HCF of 8 and 12.

F8 =1 and 8

2 and 4

F12 = 1 and 12

2 and 6

3 and 4

HCF = 4

Highest Common Factor

Example :Find the HCF of 6 and 18.

F6 =1 and 6

2 and 3

F18 = 1 and 18

2 and 9

3 and 6

HCF = 6

Highest Common Factor

Example :Find the HCF of 9 and 27.

F9 =1 and 9

3 and 3

F27 = 1 and 27

3 and 9

HCF = 9

Factors

Find the HCF for these terms

- (a)16 and 24
- 9 and 6
- 4 and 12
- 8 and 20

8

3

4

4

Factors

When finding the Highest Common Factor for

algebraic terms, treat each part of the term

separately

Example

Find the highest common factor of

4x and 24x

Step 1 : Find the HCF of the first part of the term

4

Step 2 : Find what is common in the second part of the term

x

HCF = 4x

Step 3 : Bring both terms together

Factors

When finding the Highest Common Factor for

algebraic terms, treat each part of the term

separately

Example 2

Find the highest common factor of

6x and 9

Step 1 : Find the HCF of the first part of the term

3

Step 2 : Find what is common in the second part of the term

Nothing common

HCF = 3

Step 3 : Bring both terms together

Factors

Find the HCF for these terms

- (a)16x and 24x
- 9s and 6s
- 4h and 12
- 8x and 20x
- (e)ab2 and a2b

8x

3s

4

4x

ab

Factorising

Check by multiplying out the bracket to get back to where you started

Example

Factorise 3x + 15

1. Find HCF of 3x and 15, using 3 step method

3

1. HCF first part

Nothing common

2. Common factor of second part

3

3. Bring both parts together to get HCF

2.HCF goes outside the bracket

3( )

3.To see what goes inside the bracket,

divide each initial term by the HCF

3x ÷ 3 =

x

3( x + 5 )

15 ÷ 3 =

5

Factorising

Check by multiplying out the bracket to get back to where you started

Example

Factorise 6x + 24

1. Find HCF of 6x and 24, using 3 step method

6

1. HCF first part

Nothing common

2. Common factor of second part

6

3. Bring both parts together to get HCF

2.HCF goes outside the bracket

6( )

3.To see what goes inside the bracket,

divide each initial term by the HCF

6x ÷ 6 =

x

6( x + 4 )

24 ÷ 6 =

4

Factorising

Check by multiplying out the bracket to get back to where you started

Example

Factorise 8x + 12x

1. Find HCF of 8x and 12x, using 3 step method

4

1. HCF first part

x

2. Common factor of second part

4x

3. Bring both parts together to get HCF

2.HCF goes outside the bracket

4x( )

3.To see what goes inside the bracket,

divide each initial term by the HCF

8x ÷ 4x =

2

4x( 2 + 3 )

12x ÷ 4x =

3

Factorising

Check by multiplying out the bracket to get back to where you started

Example

Factorise 2x² + 4xy + 6x

1. Find HCF of 2x², 4xy and 6x using 3 step method

2

1. HCF first part

x

2. Common factor of second part

2x

3. Bring both parts together to get HCF

2.HCF goes outside the bracket

2x( )

3.To see what goes inside the bracket,

divide each initial term by the HCF

2x² ÷ 2x =

x

4xy ÷ 2x =

2y

6x ÷ 2x =

3

2x( x + 2y +3 )

Factorising

Factorise the following :

3(x + 2)

- (a)3x + 6
- 4xy – 2x
- 6a + 7a2
- (d)xy2 -xy + 4x

Be careful !

2x(2y – 1)

a(6 + 7a)

x(y2 – y + 4)