Factorisation

What is the highest common factor of 12 and 16?

(Highest Common Factor is the largest number that divides evenly into the given numbers)

• 2

• 8

• 4

• 3

What is the highest common factor of 24 and 16?

(Highest Common Factor is the largest number that divides evenly into the given numbers)

• 6

• 8

• 4

• 3

Match the following number sets to their highest common factor:)

• 12

• 24 and 36

• 13

• 200 and 150

• 8

• 39 and 26

• 5

• 20 and 25

• 50

• 16 and 8

What is the highest common binomial factor?

23 (x + 3y) + 4 (x +3y)

• (x - 3y)

• (x + y)

• (y + 3x)

• (x + 3y)

What is the highest common binomial factor?

17a (x - 3y) + 4b (x -3y)

• (x - 3y)

• (x + y)

• (y + 3x)

• (x + 3y)

Fill in the blank: 24 + 12x = 24 + __x

Fill in the blank: 15x + 18xy = 3x (5 + _y)

Hint: 3x multiplied by what gives 18xy

Fill in the blank:

16x² + 4 = 4 ( __ x² + 1)

(Hint: 4 × ___ x²= 16x²)

Answer explanation

Factorise by grouping the terms in pairs:

12x + 3y + 4ax + ay

• 4 (4x + y) + 3 (4x + y) = (5 + a) (4x + y)

• 3 (4x + y) + a (4x + y) = 3a (4x + y)

• 3 (4x + y) + a (4x + y) = (3 + a) (4x + y)

• 12x + 3y

Match the following to their factorised form:

• 10 (2x - 1y)

• 20x - 10y

• 5x (3x -1)

• 8x² - 2x

• 4x (3x + 4)

• 15x² - 5x

• 2x (4x - 1)

• 12x² + 16x

• 6 (6x + y)

• 36x + 6y