# Finding the HCF of Algebraic Expressions

In this worksheet, students find the highest common factor of two algebraic expressions.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Understand Expressions, Equations, Inequalities, Terms and Factors

Difficulty level:

### QUESTION 1 of 10

This worksheet is about finding the Highest Common Factor (HCF) of two algebraic expressions.

Example 1

Find the HCF of 3p2qr3 and 6pq3r2

Take each term in turn.

HCF of 3 and 6 is 3.
HCF of p2 and p is p.
HCF of q and q3 is q.
HCF of r3 and r2 is r2.

So, required HCF is 3pqr2.

Example 2

Find the HCF of 4y(y - 7)(7y + 4) and (y - 7)2(7y + 4)

The highest terms common to both are (y - 7) and (7y + 4).

So the HCF is (y - 7)(7y + 4)

Select the correct HCF of these two algebraic expressions

(y-5)(5y+5)2 and (y+5)(5y+5)

(5y+5)

(y-5)

Select the correct HCF of these two algebraic expressions

8p4q3r11 and 5p5q6r4

40pqr

p 4 q 3 r 4

Select the correct HCF of these two algebraic expressions

(y-6)(6y+6) 2 and (y+6)(6y+6)

(y+6)(y-6)

(6y+6)

Select the correct HCF of these two algebraic expressions

(y-3)2 (3y+3) and (y-3)3 (3y+3)

(y-3) 2 (3y+3)

(6y+6)

Select the correct HCF of these two algebraic expressions

p 5 q 6 r 4 and 4p 2 q 3 r 4

p 2qr

p 2 q 3 r 4

Select the correct HCF of these two algebraic expressions

(y-2)(2y+8) 2 and (y+2)(2y+8)

(y-3) 2 (3y+3)

(2y+8)

Select the correct HCF of these two algebraic expressions

4p q 5 r 2 and 6 p q 4

4pqr

2p q 4 r

Select the correct HCF of these two algebraic expressions

7p 5 q 4 r  and 21p  q 6 r 6

7p q 4 r

14p q 4 r

Select the correct HCF of these two algebraic expressions

2p 6 q 3 r 3 and 4p 2 q 5 r 6

8p 1 q 4 r 1

2p 2 q 3 r 3

Select the correct HCF of these two algebraic expressions

(y-4) 2 (4y+7)3 and (y-4) 3 (4y+7)

(y-4)(4y+7)

(y-4) 2 (4y+7)

• Question 1

Select the correct HCF of these two algebraic expressions

(y-5)(5y+5)2 and (y+5)(5y+5)

(5y+5)
EDDIE SAYS
The only expression that appears in both is (5y + 5)
• Question 2

Select the correct HCF of these two algebraic expressions

8p4q3r11 and 5p5q6r4

p 4 q 3 r 4
EDDIE SAYS

In each expression we have p4, q3 and r4

• Question 3

Select the correct HCF of these two algebraic expressions

(y-6)(6y+6) 2 and (y+6)(6y+6)

(6y+6)
EDDIE SAYS
The only term that appears in both expressions is (6y + 6)
• Question 4

Select the correct HCF of these two algebraic expressions

(y-3)2 (3y+3) and (y-3)3 (3y+3)

(y-3) 2 (3y+3)
EDDIE SAYS
In both expressions we have (3y + 3) and at least two lots of (y - 3)
• Question 5

Select the correct HCF of these two algebraic expressions

p 5 q 6 r 4 and 4p 2 q 3 r 4

p 2 q 3 r 4
EDDIE SAYS

In both expressions we have p2, q3 and r4

• Question 6

Select the correct HCF of these two algebraic expressions

(y-2)(2y+8) 2 and (y+2)(2y+8)

(2y+8)
EDDIE SAYS
The only term that appears in both expressions is (2y + 8)
• Question 7

Select the correct HCF of these two algebraic expressions

4p q 5 r 2 and 6 p q 4

2p q 4 r
EDDIE SAYS

In both expressions we have the number 2, p, q4 and r

• Question 8

Select the correct HCF of these two algebraic expressions

7p 5 q 4 r  and 21p  q 6 r 6

7p q 4 r
EDDIE SAYS

In both expressions we have a factor of 7 and factors of p, q5 and r

• Question 9

Select the correct HCF of these two algebraic expressions

2p 6 q 3 r 3 and 4p 2 q 5 r 6

2p 2 q 3 r 3
EDDIE SAYS

In both expressions we have factors of 2, p2, q3 and r3

• Question 10

Select the correct HCF of these two algebraic expressions

(y-4) 2 (4y+7)3 and (y-4) 3 (4y+7)

(y-4) 2 (4y+7)
EDDIE SAYS
There are a number of factors here, (y - 4) appears at least twice in both expressions (4y + 7) appears at least once in both expressions
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