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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

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

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

Factors

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.

Factors

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

Factors

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

Factors

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

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

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

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

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

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

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

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 )

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)

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